Modul 12 - Contoh Analisis Big Data

Pengantar

Data Time Series adalah data yang diperoleh dari pengamatan satu objek dari beberapa periode waktu. Misalnya data jumlah mahasiswa dari tahun ke tahun, data nilai tukar dolar terhadap rupiah, data kasus covid dari bulan januari 2020 sampai periode saat ini, dan masih banyak contoh yang lainnya. Analisis Time Series adalah suatu bentuk peramalan terhadap nilai-nilai dimasa yang akan datang yang didasarkan pada nilai-nilai pada masa lampau. Model ini biasanya digunakan untuk melakukan prediksi/peramalan. Untuk melakukan analisis time series tersebut ada banyak teknik/metode/algoritma/model yang dapat digunakan, berikut beberapa diantaranya:

1. ARIMA, digunakan untuk tipe data stationary / random
2. ETS (error, trend, seasonal), sangat mirip pendekatannya dengan prophet facebook, yaitu dengan komponen trend dan seasonality
3. Bayesian Structural Time Series (BSTS), baik digunakan ketika ada eksternal regressor (atau pengaruh eksternal dari series lain selain komponen time series itu sendiri)
4. TBATS, model yang bisa digunakan ketika memodelkan “multiple seasonality” yaitu penggunaan 2 macam efek seasonality (misal weekly dan monthly), karena secara umum time series dianggap hanya memiliki 1 tipe seasonality
5. Prophet adalah model yang dikembangkan oleh Facebook dan fokus pada komponen: trend, seasonality (bisa multiple), dan holiday effect. dll.

Secara umum ada 3 komponen time series yaitu:

• Seosonal : data musiman, data dengan pola yang berulang dengan periode yang tetap (tahun, bulan, minggu, hari, jam, detik)
• Trend : ada 2 jenis trend yaitu cendrung naik atau cendrung turun
• Error : data yang ditangkap oleh Seosonal atau trend yang tidak bisa dijelaskan.

Load Packages

# Library untuk manipulasi data
library (dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# Library untuk visualisasi data
library (ggplot2)
library (plotly)

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

# Library model time series forecasting
library (prophet)

## Loading required package: Rcpp

## Loading required package: rlang

# Library untuk split data
library (caTools)
# Library manipulasi tanggal
library (lubridate)

## 
## Attaching package: 'lubridate'

## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union

Data Preparation

Import Data

sales <- read.csv("data/train.csv")
head(sales)

Melihat struktur data

# melihat struktur dataset
glimpse (sales)

## Rows: 730,500
## Columns: 4
## $ date  <chr> "2013-01-01", "2013-01-02", "2013-01-03", "2013-01-04", "2013-01~
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ item  <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ sales <int> 13, 11, 14, 13, 10, 12, 10, 9, 12, 9, 9, 7, 10, 12, 5, 7, 16, 7,~

Exploratory Data Analysis

Menampilkan transaksi berdasarkan store

group_sales <- group_by(sales, store)
count(group_sales)

Bisa dilihat bahwa setiap store memiliki 73050 traksaksi.

Menampilkan jumlah transaksi berdasarkan tanggal

Sekarang kita akan melihat jumlah transaksi berdasarkan tanggal transaksi dan kita simpan dalam objek daily_demand

daily_demand <- sales %>% 
  group_by(date) %>% 
  summarise( 
    demand=sum(sales)
  )  
daily_demand

Menampilkan transaksi pada salah satu store

Kita akan mengambil trankasi pada salah satu store saja, misalnya pada store 3. dan kita simpan dalam objek daily_demandstore03 dan rubah data dateke type tanggal (date)

daily_demandstore03 <- sales %>% 
  filter (store == "3") %>%
  mutate (date = as.Date(date)) %>% #merubah type data date
  group_by(date) %>% 
  summarise( 
    demand=sum(sales)
  ) 
  
daily_demandstore03

Bisa dilihat bahwa data date sudah dalam type tanggal

Visualisasi Data

kita akan memvisualisasi trankasi pada store 03 dari tahun 2013 sampai 2016

plotstore03 <- daily_demandstore03 %>% 
  ggplot(aes(x = date, y = demand)) +
  geom_point(color = "tomato3", group=1) + 
  labs( 
    title = "Daily Sales", 
    subtitle = "Store 03", 
    caption = "1C Company", 
    x = "Date", 
    y = "Total Sales" 
  ) + 
  theme_minimal() 

ggplotly(plotstore03)

Membuat Objek Time Series dengan Model Prophet

Data yang digunakan yaitu data permintaan harian di Store 3 yang sudah disimpan pada objek daily_demandstore03

daily_demandstore03

Menyiapkan data

Untuk menggunakan algoritma/model Prophet pertama-tama yang harus dilakukan adalah menyiapkan data frame dengan format: ds untuk menyimpan tanggal, dan y untuk menyimpan dari nilai yang akan prediksi.

# Menyiapkan data
train_daily_3 <- daily_demandstore03 %>% 
  rename(
    ds = "date",
    y = "demand"
    )
glimpse(train_daily_3)

## Rows: 1,461
## Columns: 2
## $ ds <date> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0~
## $ y  <int> 1588, 1538, 1635, 1741, 1887, 1956, 1313, 1538, 1633, 1677, 1831, 1~

Fit Model Data Training

Melakukan pemodelan data training dengan menggunakan fungsi fit.prophet() dimana sebelumnya kita harus menentukan seasonality nya. dalam kasus ini kita mengggunakan daily.seasonality

# fitting model data training
model_ts <- prophet(daily.seasonality = TRUE, seasonality_prior_scale=0.1) %>% 
  fit.prophet(train_daily_3)
model_ts

## $growth
## [1] "linear"
## 
## $changepoints
##  [1] "2013-02-17 GMT" "2013-04-04 GMT" "2013-05-21 GMT" "2013-07-07 GMT"
##  [5] "2013-08-22 GMT" "2013-10-08 GMT" "2013-11-24 GMT" "2014-01-09 GMT"
##  [9] "2014-02-25 GMT" "2014-04-13 GMT" "2014-05-29 GMT" "2014-07-15 GMT"
## [13] "2014-08-31 GMT" "2014-10-17 GMT" "2014-12-02 GMT" "2015-01-18 GMT"
## [17] "2015-03-06 GMT" "2015-04-21 GMT" "2015-06-07 GMT" "2015-07-24 GMT"
## [21] "2015-09-08 GMT" "2015-10-25 GMT" "2015-12-11 GMT" "2016-01-26 GMT"
## [25] "2016-03-13 GMT"
## 
## $n.changepoints
## [1] 25
## 
## $changepoint.range
## [1] 0.8
## 
## $yearly.seasonality
## [1] "auto"
## 
## $weekly.seasonality
## [1] "auto"
## 
## $daily.seasonality
## [1] TRUE
## 
## $holidays
## NULL
## 
## $seasonality.mode
## [1] "additive"
## 
## $seasonality.prior.scale
## [1] 10
## 
## $changepoint.prior.scale
## [1] 0.05
## 
## $holidays.prior.scale
## [1] 10
## 
## $mcmc.samples
## [1] 0
## 
## $interval.width
## [1] 0.8
## 
## $uncertainty.samples
## [1] 1000
## 
## $specified.changepoints
## [1] FALSE
## 
## $start
## [1] "2013-01-01 GMT"
## 
## $y.scale
## [1] 5004
## 
## $logistic.floor
## [1] FALSE
## 
## $t.scale
## [1] 126144000
## 
## $changepoints.t
##  [1] 0.03219178 0.06369863 0.09589041 0.12808219 0.15958904 0.19178082
##  [7] 0.22397260 0.25547945 0.28767123 0.31986301 0.35136986 0.38356164
## [13] 0.41575342 0.44794521 0.47945205 0.51164384 0.54383562 0.57534247
## [19] 0.60753425 0.63972603 0.67123288 0.70342466 0.73561644 0.76712329
## [25] 0.79931507
## 
## $seasonalities
## $seasonalities$yearly
## $seasonalities$yearly$period
## [1] 365.25
## 
## $seasonalities$yearly$fourier.order
## [1] 10
## 
## $seasonalities$yearly$prior.scale
## [1] 10
## 
## $seasonalities$yearly$mode
## [1] "additive"
## 
## $seasonalities$yearly$condition.name
## NULL
## 
## 
## $seasonalities$weekly
## $seasonalities$weekly$period
## [1] 7
## 
## $seasonalities$weekly$fourier.order
## [1] 3
## 
## $seasonalities$weekly$prior.scale
## [1] 10
## 
## $seasonalities$weekly$mode
## [1] "additive"
## 
## $seasonalities$weekly$condition.name
## NULL
## 
## 
## $seasonalities$daily
## $seasonalities$daily$period
## [1] 1
## 
## $seasonalities$daily$fourier.order
## [1] 4
## 
## $seasonalities$daily$prior.scale
## [1] 10
## 
## $seasonalities$daily$mode
## [1] "additive"
## 
## $seasonalities$daily$condition.name
## NULL
## 
## 
## 
## $extra_regressors
## list()
## 
## $country_holidays
## NULL
## 
## $stan.fit
## $stan.fit$par
## $stan.fit$par$k
## [1] -0.3295687
## 
## $stan.fit$par$m
## [1] 0.3550251
## 
## $stan.fit$par$delta
##  [1]  1.256203e-07 -2.981828e-08  2.662971e-01  4.727642e-01  1.918457e-01
##  [6] -1.123155e-07  5.084654e-08 -2.085096e-01 -2.661333e-01  2.654932e-08
## [11] -3.862036e-09  1.096295e-07 -4.993257e-09 -1.140498e-02 -2.853337e-02
## [16] -2.476382e-08  1.702067e-07  7.699039e-03  3.470921e-03  4.823478e-02
## [21]  7.679313e-02  2.522520e-02  3.485977e-08  3.816875e-08 -6.489775e-02
## 
## $stan.fit$par$sigma_obs
## [1] 0.02706113
## 
## $stan.fit$par$beta
##  [1] -1.495432e-02 -1.393878e-01 -2.409588e-02 -7.911498e-03 -1.775391e-02
##  [6] -2.432144e-02  7.720784e-03 -8.146249e-03  6.691417e-03 -1.189065e-02
## [11]  1.537089e-02  3.035046e-03  3.266428e-03  9.648419e-03  4.178968e-03
## [16]  5.075157e-03 -7.409245e-03  5.949041e-03 -4.866335e-03 -4.556570e-04
## [21]  7.696754e-02 -2.570954e-03 -4.462192e-02 -9.995636e-03  4.729545e-02
## [26]  6.687884e-03 -5.301163e-11  3.808422e-02 -1.060233e-10  3.808422e-02
## [31] -2.660458e-11  3.808422e-02 -2.120465e-10  3.808422e-02
## 
## $stan.fit$par$trend
##    [1] 0.3550251 0.3547994 0.3545736 0.3543479 0.3541222 0.3538964 0.3536707
##    [8] 0.3534450 0.3532192 0.3529935 0.3527678 0.3525420 0.3523163 0.3520906
##   [15] 0.3518649 0.3516391 0.3514134 0.3511877 0.3509619 0.3507362 0.3505105
##   [22] 0.3502847 0.3500590 0.3498333 0.3496075 0.3493818 0.3491561 0.3489303
##   [29] 0.3487046 0.3484789 0.3482531 0.3480274 0.3478017 0.3475759 0.3473502
##   [36] 0.3471245 0.3468987 0.3466730 0.3464473 0.3462216 0.3459958 0.3457701
##   [43] 0.3455444 0.3453186 0.3450929 0.3448672 0.3446414 0.3444157 0.3441900
##   [50] 0.3439642 0.3437385 0.3435128 0.3432870 0.3430613 0.3428356 0.3426098
##   [57] 0.3423841 0.3421584 0.3419326 0.3417069 0.3414812 0.3412555 0.3410297
##   [64] 0.3408040 0.3405783 0.3403525 0.3401268 0.3399011 0.3396753 0.3394496
##   [71] 0.3392239 0.3389981 0.3387724 0.3385467 0.3383209 0.3380952 0.3378695
##   [78] 0.3376437 0.3374180 0.3371923 0.3369665 0.3367408 0.3365151 0.3362893
##   [85] 0.3360636 0.3358379 0.3356122 0.3353864 0.3351607 0.3349350 0.3347092
##   [92] 0.3344835 0.3342578 0.3340320 0.3338063 0.3335806 0.3333548 0.3331291
##   [99] 0.3329034 0.3326776 0.3324519 0.3322262 0.3320004 0.3317747 0.3315490
##  [106] 0.3313232 0.3310975 0.3308718 0.3306461 0.3304203 0.3301946 0.3299689
##  [113] 0.3297431 0.3295174 0.3292917 0.3290659 0.3288402 0.3286145 0.3283887
##  [120] 0.3281630 0.3279373 0.3277115 0.3274858 0.3272601 0.3270343 0.3268086
##  [127] 0.3265829 0.3263571 0.3261314 0.3259057 0.3256799 0.3254542 0.3252285
##  [134] 0.3250028 0.3247770 0.3245513 0.3243256 0.3240998 0.3238741 0.3236484
##  [141] 0.3234226 0.3233793 0.3233360 0.3232926 0.3232493 0.3232059 0.3231626
##  [148] 0.3231193 0.3230759 0.3230326 0.3229893 0.3229459 0.3229026 0.3228593
##  [155] 0.3228159 0.3227726 0.3227292 0.3226859 0.3226426 0.3225992 0.3225559
##  [162] 0.3225126 0.3224692 0.3224259 0.3223826 0.3223392 0.3222959 0.3222525
##  [169] 0.3222092 0.3221659 0.3221225 0.3220792 0.3220359 0.3219925 0.3219492
##  [176] 0.3219058 0.3218625 0.3218192 0.3217758 0.3217325 0.3216892 0.3216458
##  [183] 0.3216025 0.3215592 0.3215158 0.3214725 0.3214291 0.3213858 0.3216663
##  [190] 0.3219468 0.3222272 0.3225077 0.3227882 0.3230687 0.3233491 0.3236296
##  [197] 0.3239101 0.3241906 0.3244710 0.3247515 0.3250320 0.3253125 0.3255929
##  [204] 0.3258734 0.3261539 0.3264343 0.3267148 0.3269953 0.3272758 0.3275562
##  [211] 0.3278367 0.3281172 0.3283977 0.3286781 0.3289586 0.3292391 0.3295196
##  [218] 0.3298000 0.3300805 0.3303610 0.3306415 0.3309219 0.3312024 0.3314829
##  [225] 0.3317634 0.3320438 0.3323243 0.3326048 0.3328853 0.3331657 0.3334462
##  [232] 0.3337267 0.3340072 0.3342876 0.3346995 0.3351114 0.3355233 0.3359351
##  [239] 0.3363470 0.3367589 0.3371708 0.3375826 0.3379945 0.3384064 0.3388183
##  [246] 0.3392301 0.3396420 0.3400539 0.3404658 0.3408776 0.3412895 0.3417014
##  [253] 0.3421133 0.3425251 0.3429370 0.3433489 0.3437608 0.3441726 0.3445845
##  [260] 0.3449964 0.3454083 0.3458201 0.3462320 0.3466439 0.3470558 0.3474677
##  [267] 0.3478795 0.3482914 0.3487033 0.3491152 0.3495270 0.3499389 0.3503508
##  [274] 0.3507627 0.3511745 0.3515864 0.3519983 0.3524102 0.3528220 0.3532339
##  [281] 0.3536458 0.3540577 0.3544695 0.3548814 0.3552933 0.3557052 0.3561170
##  [288] 0.3565289 0.3569408 0.3573527 0.3577645 0.3581764 0.3585883 0.3590002
##  [295] 0.3594120 0.3598239 0.3602358 0.3606477 0.3610595 0.3614714 0.3618833
##  [302] 0.3622952 0.3627070 0.3631189 0.3635308 0.3639427 0.3643546 0.3647664
##  [309] 0.3651783 0.3655902 0.3660021 0.3664139 0.3668258 0.3672377 0.3676496
##  [316] 0.3680614 0.3684733 0.3688852 0.3692971 0.3697089 0.3701208 0.3705327
##  [323] 0.3709446 0.3713564 0.3717683 0.3721802 0.3725921 0.3730039 0.3734158
##  [330] 0.3738277 0.3742396 0.3746514 0.3750633 0.3754752 0.3758871 0.3762989
##  [337] 0.3767108 0.3771227 0.3775346 0.3779464 0.3783583 0.3787702 0.3791821
##  [344] 0.3795939 0.3800058 0.3804177 0.3808296 0.3812414 0.3816533 0.3820652
##  [351] 0.3824771 0.3828890 0.3833008 0.3837127 0.3841246 0.3845365 0.3849483
##  [358] 0.3853602 0.3857721 0.3861840 0.3865958 0.3870077 0.3874196 0.3878315
##  [365] 0.3882433 0.3886552 0.3890671 0.3894790 0.3898908 0.3903027 0.3907146
##  [372] 0.3911265 0.3915383 0.3919502 0.3922193 0.3924883 0.3927574 0.3930265
##  [379] 0.3932955 0.3935646 0.3938336 0.3941027 0.3943718 0.3946408 0.3949099
##  [386] 0.3951789 0.3954480 0.3957171 0.3959861 0.3962552 0.3965242 0.3967933
##  [393] 0.3970624 0.3973314 0.3976005 0.3978696 0.3981386 0.3984077 0.3986767
##  [400] 0.3989458 0.3992149 0.3994839 0.3997530 0.4000220 0.4002911 0.4005602
##  [407] 0.4008292 0.4010983 0.4013673 0.4016364 0.4019055 0.4021745 0.4024436
##  [414] 0.4027126 0.4029817 0.4032508 0.4035198 0.4037889 0.4040580 0.4043270
##  [421] 0.4045961 0.4046829 0.4047696 0.4048564 0.4049432 0.4050300 0.4051167
##  [428] 0.4052035 0.4052903 0.4053771 0.4054638 0.4055506 0.4056374 0.4057242
##  [435] 0.4058110 0.4058977 0.4059845 0.4060713 0.4061581 0.4062448 0.4063316
##  [442] 0.4064184 0.4065052 0.4065920 0.4066787 0.4067655 0.4068523 0.4069391
##  [449] 0.4070258 0.4071126 0.4071994 0.4072862 0.4073730 0.4074597 0.4075465
##  [456] 0.4076333 0.4077201 0.4078068 0.4078936 0.4079804 0.4080672 0.4081540
##  [463] 0.4082407 0.4083275 0.4084143 0.4085011 0.4085878 0.4086746 0.4087614
##  [470] 0.4088482 0.4089350 0.4090217 0.4091085 0.4091953 0.4092821 0.4093688
##  [477] 0.4094556 0.4095424 0.4096292 0.4097160 0.4098027 0.4098895 0.4099763
##  [484] 0.4100631 0.4101498 0.4102366 0.4103234 0.4104102 0.4104970 0.4105837
##  [491] 0.4106705 0.4107573 0.4108441 0.4109308 0.4110176 0.4111044 0.4111912
##  [498] 0.4112780 0.4113647 0.4114515 0.4115383 0.4116251 0.4117118 0.4117986
##  [505] 0.4118854 0.4119722 0.4120590 0.4121457 0.4122325 0.4123193 0.4124061
##  [512] 0.4124928 0.4125796 0.4126664 0.4127532 0.4128400 0.4129267 0.4130135
##  [519] 0.4131003 0.4131871 0.4132738 0.4133606 0.4134474 0.4135342 0.4136210
##  [526] 0.4137077 0.4137945 0.4138813 0.4139681 0.4140548 0.4141416 0.4142284
##  [533] 0.4143152 0.4144020 0.4144887 0.4145755 0.4146623 0.4147491 0.4148358
##  [540] 0.4149226 0.4150094 0.4150962 0.4151830 0.4152697 0.4153565 0.4154433
##  [547] 0.4155301 0.4156168 0.4157036 0.4157904 0.4158772 0.4159640 0.4160507
##  [554] 0.4161375 0.4162243 0.4163111 0.4163978 0.4164846 0.4165714 0.4166582
##  [561] 0.4167450 0.4168317 0.4169185 0.4170053 0.4170921 0.4171788 0.4172656
##  [568] 0.4173524 0.4174392 0.4175260 0.4176127 0.4176995 0.4177863 0.4178731
##  [575] 0.4179598 0.4180466 0.4181334 0.4182202 0.4183070 0.4183937 0.4184805
##  [582] 0.4185673 0.4186541 0.4187408 0.4188276 0.4189144 0.4190012 0.4190880
##  [589] 0.4191747 0.4192615 0.4193483 0.4194351 0.4195218 0.4196086 0.4196954
##  [596] 0.4197822 0.4198690 0.4199557 0.4200425 0.4201293 0.4202161 0.4203028
##  [603] 0.4203896 0.4204764 0.4205632 0.4206500 0.4207367 0.4208235 0.4209103
##  [610] 0.4209971 0.4210838 0.4211706 0.4212574 0.4213442 0.4214310 0.4215177
##  [617] 0.4216045 0.4216913 0.4217781 0.4218648 0.4219516 0.4220384 0.4221252
##  [624] 0.4222120 0.4222987 0.4223855 0.4224723 0.4225591 0.4226458 0.4227326
##  [631] 0.4228194 0.4229062 0.4229930 0.4230797 0.4231665 0.4232533 0.4233401
##  [638] 0.4234268 0.4235136 0.4236004 0.4236872 0.4237740 0.4238607 0.4239475
##  [645] 0.4240343 0.4241211 0.4242078 0.4242946 0.4243814 0.4244682 0.4245550
##  [652] 0.4246417 0.4247285 0.4248153 0.4249021 0.4249810 0.4250600 0.4251390
##  [659] 0.4252179 0.4252969 0.4253759 0.4254548 0.4255338 0.4256128 0.4256917
##  [666] 0.4257707 0.4258497 0.4259286 0.4260076 0.4260866 0.4261655 0.4262445
##  [673] 0.4263235 0.4264024 0.4264814 0.4265604 0.4266393 0.4267183 0.4267973
##  [680] 0.4268762 0.4269552 0.4270342 0.4271131 0.4271921 0.4272711 0.4273500
##  [687] 0.4274290 0.4275080 0.4275869 0.4276659 0.4277449 0.4278238 0.4279028
##  [694] 0.4279818 0.4280607 0.4281397 0.4282187 0.4282976 0.4283766 0.4284555
##  [701] 0.4285345 0.4285939 0.4286534 0.4287128 0.4287722 0.4288316 0.4288911
##  [708] 0.4289505 0.4290099 0.4290693 0.4291287 0.4291882 0.4292476 0.4293070
##  [715] 0.4293664 0.4294259 0.4294853 0.4295447 0.4296041 0.4296635 0.4297230
##  [722] 0.4297824 0.4298418 0.4299012 0.4299607 0.4300201 0.4300795 0.4301389
##  [729] 0.4301984 0.4302578 0.4303172 0.4303766 0.4304360 0.4304955 0.4305549
##  [736] 0.4306143 0.4306737 0.4307332 0.4307926 0.4308520 0.4309114 0.4309708
##  [743] 0.4310303 0.4310897 0.4311491 0.4312085 0.4312680 0.4313274 0.4313868
##  [750] 0.4314462 0.4315057 0.4315651 0.4316245 0.4316839 0.4317433 0.4318028
##  [757] 0.4318622 0.4319216 0.4319810 0.4320405 0.4320999 0.4321593 0.4322187
##  [764] 0.4322781 0.4323376 0.4323970 0.4324564 0.4325158 0.4325753 0.4326347
##  [771] 0.4326941 0.4327535 0.4328130 0.4328724 0.4329318 0.4329912 0.4330506
##  [778] 0.4331101 0.4331695 0.4332289 0.4332883 0.4333478 0.4334072 0.4334666
##  [785] 0.4335260 0.4335855 0.4336449 0.4337043 0.4337637 0.4338231 0.4338826
##  [792] 0.4339420 0.4340014 0.4340608 0.4341203 0.4341797 0.4342391 0.4342985
##  [799] 0.4343579 0.4344174 0.4344768 0.4345362 0.4345956 0.4346551 0.4347145
##  [806] 0.4347739 0.4348333 0.4348928 0.4349522 0.4350116 0.4350710 0.4351304
##  [813] 0.4351899 0.4352493 0.4353087 0.4353681 0.4354276 0.4354870 0.4355464
##  [820] 0.4356058 0.4356653 0.4357247 0.4357841 0.4358435 0.4359029 0.4359624
##  [827] 0.4360218 0.4360812 0.4361406 0.4362001 0.4362595 0.4363189 0.4363783
##  [834] 0.4364377 0.4364972 0.4365566 0.4366160 0.4366754 0.4367349 0.4367943
##  [841] 0.4368537 0.4369184 0.4369831 0.4370478 0.4371125 0.4371772 0.4372419
##  [848] 0.4373066 0.4373713 0.4374360 0.4375007 0.4375654 0.4376301 0.4376948
##  [855] 0.4377595 0.4378242 0.4378888 0.4379535 0.4380182 0.4380829 0.4381476
##  [862] 0.4382123 0.4382770 0.4383417 0.4384064 0.4384711 0.4385358 0.4386005
##  [869] 0.4386652 0.4387299 0.4387946 0.4388593 0.4389240 0.4389887 0.4390534
##  [876] 0.4391181 0.4391828 0.4392475 0.4393122 0.4393769 0.4394416 0.4395063
##  [883] 0.4395709 0.4396356 0.4397003 0.4397650 0.4398297 0.4398944 0.4399615
##  [890] 0.4400286 0.4400956 0.4401627 0.4402298 0.4402969 0.4403639 0.4404310
##  [897] 0.4404981 0.4405652 0.4406322 0.4406993 0.4407664 0.4408335 0.4409005
##  [904] 0.4409676 0.4410347 0.4411018 0.4411688 0.4412359 0.4413030 0.4413700
##  [911] 0.4414371 0.4415042 0.4415713 0.4416383 0.4417054 0.4417725 0.4418396
##  [918] 0.4419066 0.4419737 0.4420408 0.4421079 0.4421749 0.4422420 0.4423091
##  [925] 0.4423761 0.4424432 0.4425103 0.4425774 0.4426444 0.4427115 0.4427786
##  [932] 0.4428457 0.4429127 0.4429798 0.4430469 0.4431470 0.4432471 0.4433472
##  [939] 0.4434473 0.4435474 0.4436476 0.4437477 0.4438478 0.4439479 0.4440480
##  [946] 0.4441481 0.4442482 0.4443483 0.4444484 0.4445486 0.4446487 0.4447488
##  [953] 0.4448489 0.4449490 0.4450491 0.4451492 0.4452493 0.4453494 0.4454496
##  [960] 0.4455497 0.4456498 0.4457499 0.4458500 0.4459501 0.4460502 0.4461503
##  [967] 0.4462504 0.4463505 0.4464507 0.4465508 0.4466509 0.4467510 0.4468511
##  [974] 0.4469512 0.4470513 0.4471514 0.4472515 0.4473517 0.4474518 0.4475519
##  [981] 0.4476520 0.4478047 0.4479574 0.4481101 0.4482628 0.4484155 0.4485682
##  [988] 0.4487210 0.4488737 0.4490264 0.4491791 0.4493318 0.4494845 0.4496372
##  [995] 0.4497899 0.4499426 0.4500953 0.4502480 0.4504008 0.4505535 0.4507062
## [1002] 0.4508589 0.4510116 0.4511643 0.4513170 0.4514697 0.4516224 0.4517751
## [1009] 0.4519278 0.4520806 0.4522333 0.4523860 0.4525387 0.4526914 0.4528441
## [1016] 0.4529968 0.4531495 0.4533022 0.4534549 0.4536076 0.4537604 0.4539131
## [1023] 0.4540658 0.4542185 0.4543712 0.4545239 0.4546766 0.4548293 0.4549993
## [1030] 0.4551693 0.4553393 0.4555093 0.4556793 0.4558492 0.4560192 0.4561892
## [1037] 0.4563592 0.4565292 0.4566992 0.4568692 0.4570391 0.4572091 0.4573791
## [1044] 0.4575491 0.4577191 0.4578891 0.4580591 0.4582291 0.4583990 0.4585690
## [1051] 0.4587390 0.4589090 0.4590790 0.4592490 0.4594190 0.4595889 0.4597589
## [1058] 0.4599289 0.4600989 0.4602689 0.4604389 0.4606089 0.4607789 0.4609488
## [1065] 0.4611188 0.4612888 0.4614588 0.4616288 0.4617988 0.4619688 0.4621387
## [1072] 0.4623087 0.4624787 0.4626487 0.4628187 0.4629887 0.4631587 0.4633287
## [1079] 0.4634986 0.4636686 0.4638386 0.4640086 0.4641786 0.4643486 0.4645186
## [1086] 0.4646885 0.4648585 0.4650285 0.4651985 0.4653685 0.4655385 0.4657085
## [1093] 0.4658785 0.4660484 0.4662184 0.4663884 0.4665584 0.4667284 0.4668984
## [1100] 0.4670684 0.4672383 0.4674083 0.4675783 0.4677483 0.4679183 0.4680883
## [1107] 0.4682583 0.4684283 0.4685982 0.4687682 0.4689382 0.4691082 0.4692782
## [1114] 0.4694482 0.4696182 0.4697881 0.4699581 0.4701281 0.4702981 0.4704681
## [1121] 0.4706381 0.4708081 0.4709781 0.4711480 0.4713180 0.4714880 0.4716580
## [1128] 0.4718280 0.4719980 0.4721680 0.4723379 0.4725079 0.4726779 0.4728479
## [1135] 0.4730179 0.4731879 0.4733579 0.4735279 0.4736978 0.4738678 0.4740378
## [1142] 0.4742078 0.4743778 0.4745478 0.4747178 0.4748877 0.4750577 0.4752277
## [1149] 0.4753977 0.4755677 0.4757377 0.4759077 0.4760777 0.4762476 0.4764176
## [1156] 0.4765876 0.4767576 0.4769276 0.4770976 0.4772676 0.4774375 0.4776075
## [1163] 0.4777775 0.4779475 0.4781175 0.4782875 0.4784575 0.4786275 0.4787530
## [1170] 0.4788785 0.4790041 0.4791296 0.4792551 0.4793807 0.4795062 0.4796317
## [1177] 0.4797573 0.4798828 0.4800084 0.4801339 0.4802594 0.4803850 0.4805105
## [1184] 0.4806360 0.4807616 0.4808871 0.4810126 0.4811382 0.4812637 0.4813892
## [1191] 0.4815148 0.4816403 0.4817659 0.4818914 0.4820169 0.4821425 0.4822680
## [1198] 0.4823935 0.4825191 0.4826446 0.4827701 0.4828957 0.4830212 0.4831468
## [1205] 0.4832723 0.4833978 0.4835234 0.4836489 0.4837744 0.4839000 0.4840255
## [1212] 0.4841510 0.4842766 0.4844021 0.4845277 0.4846532 0.4847787 0.4849043
## [1219] 0.4850298 0.4851553 0.4852809 0.4854064 0.4855319 0.4856575 0.4857830
## [1226] 0.4859086 0.4860341 0.4861596 0.4862852 0.4864107 0.4865362 0.4866618
## [1233] 0.4867873 0.4869128 0.4870384 0.4871639 0.4872894 0.4874150 0.4875405
## [1240] 0.4876661 0.4877916 0.4879171 0.4880427 0.4881682 0.4882937 0.4884193
## [1247] 0.4885448 0.4886703 0.4887959 0.4889214 0.4890470 0.4891725 0.4892980
## [1254] 0.4894236 0.4895491 0.4896746 0.4898002 0.4899257 0.4900512 0.4901768
## [1261] 0.4903023 0.4904279 0.4905534 0.4906789 0.4908045 0.4909300 0.4910555
## [1268] 0.4911811 0.4913066 0.4914321 0.4915577 0.4916832 0.4918088 0.4919343
## [1275] 0.4920598 0.4921854 0.4923109 0.4924364 0.4925620 0.4926875 0.4928130
## [1282] 0.4929386 0.4930641 0.4931896 0.4933152 0.4934407 0.4935663 0.4936918
## [1289] 0.4938173 0.4939429 0.4940684 0.4941939 0.4943195 0.4944450 0.4945705
## [1296] 0.4946961 0.4948216 0.4949472 0.4950727 0.4951982 0.4953238 0.4954493
## [1303] 0.4955748 0.4957004 0.4958259 0.4959514 0.4960770 0.4962025 0.4963281
## [1310] 0.4964536 0.4965791 0.4967047 0.4968302 0.4969557 0.4970813 0.4972068
## [1317] 0.4973323 0.4974579 0.4975834 0.4977090 0.4978345 0.4979600 0.4980856
## [1324] 0.4982111 0.4983366 0.4984622 0.4985877 0.4987132 0.4988388 0.4989643
## [1331] 0.4990898 0.4992154 0.4993409 0.4994665 0.4995920 0.4997175 0.4998431
## [1338] 0.4999686 0.5000941 0.5002197 0.5003452 0.5004707 0.5005963 0.5007218
## [1345] 0.5008474 0.5009729 0.5010984 0.5012240 0.5013495 0.5014750 0.5016006
## [1352] 0.5017261 0.5018516 0.5019772 0.5021027 0.5022283 0.5023538 0.5024793
## [1359] 0.5026049 0.5027304 0.5028559 0.5029815 0.5031070 0.5032325 0.5033581
## [1366] 0.5034836 0.5036092 0.5037347 0.5038602 0.5039858 0.5041113 0.5042368
## [1373] 0.5043624 0.5044879 0.5046134 0.5047390 0.5048645 0.5049900 0.5051156
## [1380] 0.5052411 0.5053667 0.5054922 0.5056177 0.5057433 0.5058688 0.5059943
## [1387] 0.5061199 0.5062454 0.5063709 0.5064965 0.5066220 0.5067476 0.5068731
## [1394] 0.5069986 0.5071242 0.5072497 0.5073752 0.5075008 0.5076263 0.5077518
## [1401] 0.5078774 0.5080029 0.5081285 0.5082540 0.5083795 0.5085051 0.5086306
## [1408] 0.5087561 0.5088817 0.5090072 0.5091327 0.5092583 0.5093838 0.5095094
## [1415] 0.5096349 0.5097604 0.5098860 0.5100115 0.5101370 0.5102626 0.5103881
## [1422] 0.5105136 0.5106392 0.5107647 0.5108902 0.5110158 0.5111413 0.5112669
## [1429] 0.5113924 0.5115179 0.5116435 0.5117690 0.5118945 0.5120201 0.5121456
## [1436] 0.5122711 0.5123967 0.5125222 0.5126478 0.5127733 0.5128988 0.5130244
## [1443] 0.5131499 0.5132754 0.5134010 0.5135265 0.5136520 0.5137776 0.5139031
## [1450] 0.5140287 0.5141542 0.5142797 0.5144053 0.5145308 0.5146563 0.5147819
## [1457] 0.5149074 0.5150329 0.5151585 0.5152840 0.5154095
## 
## 
## $stan.fit$value
## [1] 4510.003
## 
## $stan.fit$return_code
## [1] 0
## 
## $stan.fit$theta_tilde
##               k         m     delta[1]      delta[2]  delta[3]  delta[4]
## [1,] -0.3295687 0.3550251 1.256203e-07 -2.981828e-08 0.2662971 0.4727642
##       delta[5]      delta[6]     delta[7]   delta[8]   delta[9]    delta[10]
## [1,] 0.1918457 -1.123155e-07 5.084654e-08 -0.2085096 -0.2661333 2.654932e-08
##          delta[11]    delta[12]     delta[13]   delta[14]   delta[15]
## [1,] -3.862036e-09 1.096295e-07 -4.993257e-09 -0.01140498 -0.02853337
##          delta[16]    delta[17]   delta[18]   delta[19]  delta[20]  delta[21]
## [1,] -2.476382e-08 1.702067e-07 0.007699039 0.003470921 0.04823478 0.07679313
##      delta[22]    delta[23]    delta[24]   delta[25]  sigma_obs     beta[1]
## [1,] 0.0252252 3.485977e-08 3.816875e-08 -0.06489775 0.02706113 -0.01495432
##         beta[2]     beta[3]      beta[4]     beta[5]     beta[6]     beta[7]
## [1,] -0.1393878 -0.02409588 -0.007911498 -0.01775391 -0.02432144 0.007720784
##           beta[8]     beta[9]    beta[10]   beta[11]    beta[12]    beta[13]
## [1,] -0.008146249 0.006691417 -0.01189065 0.01537089 0.003035046 0.003266428
##         beta[14]    beta[15]    beta[16]     beta[17]    beta[18]     beta[19]
## [1,] 0.009648419 0.004178968 0.005075157 -0.007409245 0.005949041 -0.004866335
##          beta[20]   beta[21]     beta[22]    beta[23]     beta[24]   beta[25]
## [1,] -0.000455657 0.07696754 -0.002570954 -0.04462192 -0.009995636 0.04729545
##         beta[26]      beta[27]   beta[28]      beta[29]   beta[30]
## [1,] 0.006687884 -5.301163e-11 0.03808422 -1.060233e-10 0.03808422
##           beta[31]   beta[32]      beta[33]   beta[34]  trend[1]  trend[2]
## [1,] -2.660458e-11 0.03808422 -2.120465e-10 0.03808422 0.3550251 0.3547994
##       trend[3]  trend[4]  trend[5]  trend[6]  trend[7] trend[8]  trend[9]
## [1,] 0.3545736 0.3543479 0.3541222 0.3538964 0.3536707 0.353445 0.3532192
##      trend[10] trend[11] trend[12] trend[13] trend[14] trend[15] trend[16]
## [1,] 0.3529935 0.3527678  0.352542 0.3523163 0.3520906 0.3518649 0.3516391
##      trend[17] trend[18] trend[19] trend[20] trend[21] trend[22] trend[23]
## [1,] 0.3514134 0.3511877 0.3509619 0.3507362 0.3505105 0.3502847  0.350059
##      trend[24] trend[25] trend[26] trend[27] trend[28] trend[29] trend[30]
## [1,] 0.3498333 0.3496075 0.3493818 0.3491561 0.3489303 0.3487046 0.3484789
##      trend[31] trend[32] trend[33] trend[34] trend[35] trend[36] trend[37]
## [1,] 0.3482531 0.3480274 0.3478017 0.3475759 0.3473502 0.3471245 0.3468987
##      trend[38] trend[39] trend[40] trend[41] trend[42] trend[43] trend[44]
## [1,]  0.346673 0.3464473 0.3462216 0.3459958 0.3457701 0.3455444 0.3453186
##      trend[45] trend[46] trend[47] trend[48] trend[49] trend[50] trend[51]
## [1,] 0.3450929 0.3448672 0.3446414 0.3444157   0.34419 0.3439642 0.3437385
##      trend[52] trend[53] trend[54] trend[55] trend[56] trend[57] trend[58]
## [1,] 0.3435128  0.343287 0.3430613 0.3428356 0.3426098 0.3423841 0.3421584
##      trend[59] trend[60] trend[61] trend[62] trend[63] trend[64] trend[65]
## [1,] 0.3419326 0.3417069 0.3414812 0.3412555 0.3410297  0.340804 0.3405783
##      trend[66] trend[67] trend[68] trend[69] trend[70] trend[71] trend[72]
## [1,] 0.3403525 0.3401268 0.3399011 0.3396753 0.3394496 0.3392239 0.3389981
##      trend[73] trend[74] trend[75] trend[76] trend[77] trend[78] trend[79]
## [1,] 0.3387724 0.3385467 0.3383209 0.3380952 0.3378695 0.3376437  0.337418
##      trend[80] trend[81] trend[82] trend[83] trend[84] trend[85] trend[86]
## [1,] 0.3371923 0.3369665 0.3367408 0.3365151 0.3362893 0.3360636 0.3358379
##      trend[87] trend[88] trend[89] trend[90] trend[91] trend[92] trend[93]
## [1,] 0.3356122 0.3353864 0.3351607  0.334935 0.3347092 0.3344835 0.3342578
##      trend[94] trend[95] trend[96] trend[97] trend[98] trend[99] trend[100]
## [1,]  0.334032 0.3338063 0.3335806 0.3333548 0.3331291 0.3329034  0.3326776
##      trend[101] trend[102] trend[103] trend[104] trend[105] trend[106]
## [1,]  0.3324519  0.3322262  0.3320004  0.3317747   0.331549  0.3313232
##      trend[107] trend[108] trend[109] trend[110] trend[111] trend[112]
## [1,]  0.3310975  0.3308718  0.3306461  0.3304203  0.3301946  0.3299689
##      trend[113] trend[114] trend[115] trend[116] trend[117] trend[118]
## [1,]  0.3297431  0.3295174  0.3292917  0.3290659  0.3288402  0.3286145
##      trend[119] trend[120] trend[121] trend[122] trend[123] trend[124]
## [1,]  0.3283887   0.328163  0.3279373  0.3277115  0.3274858  0.3272601
##      trend[125] trend[126] trend[127] trend[128] trend[129] trend[130]
## [1,]  0.3270343  0.3268086  0.3265829  0.3263571  0.3261314  0.3259057
##      trend[131] trend[132] trend[133] trend[134] trend[135] trend[136]
## [1,]  0.3256799  0.3254542  0.3252285  0.3250028   0.324777  0.3245513
##      trend[137] trend[138] trend[139] trend[140] trend[141] trend[142]
## [1,]  0.3243256  0.3240998  0.3238741  0.3236484  0.3234226  0.3233793
##      trend[143] trend[144] trend[145] trend[146] trend[147] trend[148]
## [1,]   0.323336  0.3232926  0.3232493  0.3232059  0.3231626  0.3231193
##      trend[149] trend[150] trend[151] trend[152] trend[153] trend[154]
## [1,]  0.3230759  0.3230326  0.3229893  0.3229459  0.3229026  0.3228593
##      trend[155] trend[156] trend[157] trend[158] trend[159] trend[160]
## [1,]  0.3228159  0.3227726  0.3227292  0.3226859  0.3226426  0.3225992
##      trend[161] trend[162] trend[163] trend[164] trend[165] trend[166]
## [1,]  0.3225559  0.3225126  0.3224692  0.3224259  0.3223826  0.3223392
##      trend[167] trend[168] trend[169] trend[170] trend[171] trend[172]
## [1,]  0.3222959  0.3222525  0.3222092  0.3221659  0.3221225  0.3220792
##      trend[173] trend[174] trend[175] trend[176] trend[177] trend[178]
## [1,]  0.3220359  0.3219925  0.3219492  0.3219058  0.3218625  0.3218192
##      trend[179] trend[180] trend[181] trend[182] trend[183] trend[184]
## [1,]  0.3217758  0.3217325  0.3216892  0.3216458  0.3216025  0.3215592
##      trend[185] trend[186] trend[187] trend[188] trend[189] trend[190]
## [1,]  0.3215158  0.3214725  0.3214291  0.3213858  0.3216663  0.3219468
##      trend[191] trend[192] trend[193] trend[194] trend[195] trend[196]
## [1,]  0.3222272  0.3225077  0.3227882  0.3230687  0.3233491  0.3236296
##      trend[197] trend[198] trend[199] trend[200] trend[201] trend[202]
## [1,]  0.3239101  0.3241906   0.324471  0.3247515   0.325032  0.3253125
##      trend[203] trend[204] trend[205] trend[206] trend[207] trend[208]
## [1,]  0.3255929  0.3258734  0.3261539  0.3264343  0.3267148  0.3269953
##      trend[209] trend[210] trend[211] trend[212] trend[213] trend[214]
## [1,]  0.3272758  0.3275562  0.3278367  0.3281172  0.3283977  0.3286781
##      trend[215] trend[216] trend[217] trend[218] trend[219] trend[220]
## [1,]  0.3289586  0.3292391  0.3295196     0.3298  0.3300805   0.330361
##      trend[221] trend[222] trend[223] trend[224] trend[225] trend[226]
## [1,]  0.3306415  0.3309219  0.3312024  0.3314829  0.3317634  0.3320438
##      trend[227] trend[228] trend[229] trend[230] trend[231] trend[232]
## [1,]  0.3323243  0.3326048  0.3328853  0.3331657  0.3334462  0.3337267
##      trend[233] trend[234] trend[235] trend[236] trend[237] trend[238]
## [1,]  0.3340072  0.3342876  0.3346995  0.3351114  0.3355233  0.3359351
##      trend[239] trend[240] trend[241] trend[242] trend[243] trend[244]
## [1,]   0.336347  0.3367589  0.3371708  0.3375826  0.3379945  0.3384064
##      trend[245] trend[246] trend[247] trend[248] trend[249] trend[250]
## [1,]  0.3388183  0.3392301   0.339642  0.3400539  0.3404658  0.3408776
##      trend[251] trend[252] trend[253] trend[254] trend[255] trend[256]
## [1,]  0.3412895  0.3417014  0.3421133  0.3425251   0.342937  0.3433489
##      trend[257] trend[258] trend[259] trend[260] trend[261] trend[262]
## [1,]  0.3437608  0.3441726  0.3445845  0.3449964  0.3454083  0.3458201
##      trend[263] trend[264] trend[265] trend[266] trend[267] trend[268]
## [1,]   0.346232  0.3466439  0.3470558  0.3474677  0.3478795  0.3482914
##      trend[269] trend[270] trend[271] trend[272] trend[273] trend[274]
## [1,]  0.3487033  0.3491152   0.349527  0.3499389  0.3503508  0.3507627
##      trend[275] trend[276] trend[277] trend[278] trend[279] trend[280]
## [1,]  0.3511745  0.3515864  0.3519983  0.3524102   0.352822  0.3532339
##      trend[281] trend[282] trend[283] trend[284] trend[285] trend[286]
## [1,]  0.3536458  0.3540577  0.3544695  0.3548814  0.3552933  0.3557052
##      trend[287] trend[288] trend[289] trend[290] trend[291] trend[292]
## [1,]   0.356117  0.3565289  0.3569408  0.3573527  0.3577645  0.3581764
##      trend[293] trend[294] trend[295] trend[296] trend[297] trend[298]
## [1,]  0.3585883  0.3590002   0.359412  0.3598239  0.3602358  0.3606477
##      trend[299] trend[300] trend[301] trend[302] trend[303] trend[304]
## [1,]  0.3610595  0.3614714  0.3618833  0.3622952   0.362707  0.3631189
##      trend[305] trend[306] trend[307] trend[308] trend[309] trend[310]
## [1,]  0.3635308  0.3639427  0.3643546  0.3647664  0.3651783  0.3655902
##      trend[311] trend[312] trend[313] trend[314] trend[315] trend[316]
## [1,]  0.3660021  0.3664139  0.3668258  0.3672377  0.3676496  0.3680614
##      trend[317] trend[318] trend[319] trend[320] trend[321] trend[322]
## [1,]  0.3684733  0.3688852  0.3692971  0.3697089  0.3701208  0.3705327
##      trend[323] trend[324] trend[325] trend[326] trend[327] trend[328]
## [1,]  0.3709446  0.3713564  0.3717683  0.3721802  0.3725921  0.3730039
##      trend[329] trend[330] trend[331] trend[332] trend[333] trend[334]
## [1,]  0.3734158  0.3738277  0.3742396  0.3746514  0.3750633  0.3754752
##      trend[335] trend[336] trend[337] trend[338] trend[339] trend[340]
## [1,]  0.3758871  0.3762989  0.3767108  0.3771227  0.3775346  0.3779464
##      trend[341] trend[342] trend[343] trend[344] trend[345] trend[346]
## [1,]  0.3783583  0.3787702  0.3791821  0.3795939  0.3800058  0.3804177
##      trend[347] trend[348] trend[349] trend[350] trend[351] trend[352]
## [1,]  0.3808296  0.3812414  0.3816533  0.3820652  0.3824771   0.382889
##      trend[353] trend[354] trend[355] trend[356] trend[357] trend[358]
## [1,]  0.3833008  0.3837127  0.3841246  0.3845365  0.3849483  0.3853602
##      trend[359] trend[360] trend[361] trend[362] trend[363] trend[364]
## [1,]  0.3857721   0.386184  0.3865958  0.3870077  0.3874196  0.3878315
##      trend[365] trend[366] trend[367] trend[368] trend[369] trend[370]
## [1,]  0.3882433  0.3886552  0.3890671   0.389479  0.3898908  0.3903027
##      trend[371] trend[372] trend[373] trend[374] trend[375] trend[376]
## [1,]  0.3907146  0.3911265  0.3915383  0.3919502  0.3922193  0.3924883
##      trend[377] trend[378] trend[379] trend[380] trend[381] trend[382]
## [1,]  0.3927574  0.3930265  0.3932955  0.3935646  0.3938336  0.3941027
##      trend[383] trend[384] trend[385] trend[386] trend[387] trend[388]
## [1,]  0.3943718  0.3946408  0.3949099  0.3951789   0.395448  0.3957171
##      trend[389] trend[390] trend[391] trend[392] trend[393] trend[394]
## [1,]  0.3959861  0.3962552  0.3965242  0.3967933  0.3970624  0.3973314
##      trend[395] trend[396] trend[397] trend[398] trend[399] trend[400]
## [1,]  0.3976005  0.3978696  0.3981386  0.3984077  0.3986767  0.3989458
##      trend[401] trend[402] trend[403] trend[404] trend[405] trend[406]
## [1,]  0.3992149  0.3994839   0.399753   0.400022  0.4002911  0.4005602
##      trend[407] trend[408] trend[409] trend[410] trend[411] trend[412]
## [1,]  0.4008292  0.4010983  0.4013673  0.4016364  0.4019055  0.4021745
##      trend[413] trend[414] trend[415] trend[416] trend[417] trend[418]
## [1,]  0.4024436  0.4027126  0.4029817  0.4032508  0.4035198  0.4037889
##      trend[419] trend[420] trend[421] trend[422] trend[423] trend[424]
## [1,]   0.404058   0.404327  0.4045961  0.4046829  0.4047696  0.4048564
##      trend[425] trend[426] trend[427] trend[428] trend[429] trend[430]
## [1,]  0.4049432    0.40503  0.4051167  0.4052035  0.4052903  0.4053771
##      trend[431] trend[432] trend[433] trend[434] trend[435] trend[436]
## [1,]  0.4054638  0.4055506  0.4056374  0.4057242   0.405811  0.4058977
##      trend[437] trend[438] trend[439] trend[440] trend[441] trend[442]
## [1,]  0.4059845  0.4060713  0.4061581  0.4062448  0.4063316  0.4064184
##      trend[443] trend[444] trend[445] trend[446] trend[447] trend[448]
## [1,]  0.4065052   0.406592  0.4066787  0.4067655  0.4068523  0.4069391
##      trend[449] trend[450] trend[451] trend[452] trend[453] trend[454]
## [1,]  0.4070258  0.4071126  0.4071994  0.4072862   0.407373  0.4074597
##      trend[455] trend[456] trend[457] trend[458] trend[459] trend[460]
## [1,]  0.4075465  0.4076333  0.4077201  0.4078068  0.4078936  0.4079804
##      trend[461] trend[462] trend[463] trend[464] trend[465] trend[466]
## [1,]  0.4080672   0.408154  0.4082407  0.4083275  0.4084143  0.4085011
##      trend[467] trend[468] trend[469] trend[470] trend[471] trend[472]
## [1,]  0.4085878  0.4086746  0.4087614  0.4088482   0.408935  0.4090217
##      trend[473] trend[474] trend[475] trend[476] trend[477] trend[478]
## [1,]  0.4091085  0.4091953  0.4092821  0.4093688  0.4094556  0.4095424
##      trend[479] trend[480] trend[481] trend[482] trend[483] trend[484]
## [1,]  0.4096292   0.409716  0.4098027  0.4098895  0.4099763  0.4100631
##      trend[485] trend[486] trend[487] trend[488] trend[489] trend[490]
## [1,]  0.4101498  0.4102366  0.4103234  0.4104102   0.410497  0.4105837
##      trend[491] trend[492] trend[493] trend[494] trend[495] trend[496]
## [1,]  0.4106705  0.4107573  0.4108441  0.4109308  0.4110176  0.4111044
##      trend[497] trend[498] trend[499] trend[500] trend[501] trend[502]
## [1,]  0.4111912   0.411278  0.4113647  0.4114515  0.4115383  0.4116251
##      trend[503] trend[504] trend[505] trend[506] trend[507] trend[508]
## [1,]  0.4117118  0.4117986  0.4118854  0.4119722   0.412059  0.4121457
##      trend[509] trend[510] trend[511] trend[512] trend[513] trend[514]
## [1,]  0.4122325  0.4123193  0.4124061  0.4124928  0.4125796  0.4126664
##      trend[515] trend[516] trend[517] trend[518] trend[519] trend[520]
## [1,]  0.4127532    0.41284  0.4129267  0.4130135  0.4131003  0.4131871
##      trend[521] trend[522] trend[523] trend[524] trend[525] trend[526]
## [1,]  0.4132738  0.4133606  0.4134474  0.4135342   0.413621  0.4137077
##      trend[527] trend[528] trend[529] trend[530] trend[531] trend[532]
## [1,]  0.4137945  0.4138813  0.4139681  0.4140548  0.4141416  0.4142284
##      trend[533] trend[534] trend[535] trend[536] trend[537] trend[538]
## [1,]  0.4143152   0.414402  0.4144887  0.4145755  0.4146623  0.4147491
##      trend[539] trend[540] trend[541] trend[542] trend[543] trend[544]
## [1,]  0.4148358  0.4149226  0.4150094  0.4150962   0.415183  0.4152697
##      trend[545] trend[546] trend[547] trend[548] trend[549] trend[550]
## [1,]  0.4153565  0.4154433  0.4155301  0.4156168  0.4157036  0.4157904
##      trend[551] trend[552] trend[553] trend[554] trend[555] trend[556]
## [1,]  0.4158772   0.415964  0.4160507  0.4161375  0.4162243  0.4163111
##      trend[557] trend[558] trend[559] trend[560] trend[561] trend[562]
## [1,]  0.4163978  0.4164846  0.4165714  0.4166582   0.416745  0.4168317
##      trend[563] trend[564] trend[565] trend[566] trend[567] trend[568]
## [1,]  0.4169185  0.4170053  0.4170921  0.4171788  0.4172656  0.4173524
##      trend[569] trend[570] trend[571] trend[572] trend[573] trend[574]
## [1,]  0.4174392   0.417526  0.4176127  0.4176995  0.4177863  0.4178731
##      trend[575] trend[576] trend[577] trend[578] trend[579] trend[580]
## [1,]  0.4179598  0.4180466  0.4181334  0.4182202   0.418307  0.4183937
##      trend[581] trend[582] trend[583] trend[584] trend[585] trend[586]
## [1,]  0.4184805  0.4185673  0.4186541  0.4187408  0.4188276  0.4189144
##      trend[587] trend[588] trend[589] trend[590] trend[591] trend[592]
## [1,]  0.4190012   0.419088  0.4191747  0.4192615  0.4193483  0.4194351
##      trend[593] trend[594] trend[595] trend[596] trend[597] trend[598]
## [1,]  0.4195218  0.4196086  0.4196954  0.4197822   0.419869  0.4199557
##      trend[599] trend[600] trend[601] trend[602] trend[603] trend[604]
## [1,]  0.4200425  0.4201293  0.4202161  0.4203028  0.4203896  0.4204764
##      trend[605] trend[606] trend[607] trend[608] trend[609] trend[610]
## [1,]  0.4205632    0.42065  0.4207367  0.4208235  0.4209103  0.4209971
##      trend[611] trend[612] trend[613] trend[614] trend[615] trend[616]
## [1,]  0.4210838  0.4211706  0.4212574  0.4213442   0.421431  0.4215177
##      trend[617] trend[618] trend[619] trend[620] trend[621] trend[622]
## [1,]  0.4216045  0.4216913  0.4217781  0.4218648  0.4219516  0.4220384
##      trend[623] trend[624] trend[625] trend[626] trend[627] trend[628]
## [1,]  0.4221252   0.422212  0.4222987  0.4223855  0.4224723  0.4225591
##      trend[629] trend[630] trend[631] trend[632] trend[633] trend[634]
## [1,]  0.4226458  0.4227326  0.4228194  0.4229062   0.422993  0.4230797
##      trend[635] trend[636] trend[637] trend[638] trend[639] trend[640]
## [1,]  0.4231665  0.4232533  0.4233401  0.4234268  0.4235136  0.4236004
##      trend[641] trend[642] trend[643] trend[644] trend[645] trend[646]
## [1,]  0.4236872   0.423774  0.4238607  0.4239475  0.4240343  0.4241211
##      trend[647] trend[648] trend[649] trend[650] trend[651] trend[652]
## [1,]  0.4242078  0.4242946  0.4243814  0.4244682   0.424555  0.4246417
##      trend[653] trend[654] trend[655] trend[656] trend[657] trend[658]
## [1,]  0.4247285  0.4248153  0.4249021   0.424981    0.42506   0.425139
##      trend[659] trend[660] trend[661] trend[662] trend[663] trend[664]
## [1,]  0.4252179  0.4252969  0.4253759  0.4254548  0.4255338  0.4256128
##      trend[665] trend[666] trend[667] trend[668] trend[669] trend[670]
## [1,]  0.4256917  0.4257707  0.4258497  0.4259286  0.4260076  0.4260866
##      trend[671] trend[672] trend[673] trend[674] trend[675] trend[676]
## [1,]  0.4261655  0.4262445  0.4263235  0.4264024  0.4264814  0.4265604
##      trend[677] trend[678] trend[679] trend[680] trend[681] trend[682]
## [1,]  0.4266393  0.4267183  0.4267973  0.4268762  0.4269552  0.4270342
##      trend[683] trend[684] trend[685] trend[686] trend[687] trend[688]
## [1,]  0.4271131  0.4271921  0.4272711    0.42735   0.427429   0.427508
##      trend[689] trend[690] trend[691] trend[692] trend[693] trend[694]
## [1,]  0.4275869  0.4276659  0.4277449  0.4278238  0.4279028  0.4279818
##      trend[695] trend[696] trend[697] trend[698] trend[699] trend[700]
## [1,]  0.4280607  0.4281397  0.4282187  0.4282976  0.4283766  0.4284555
##      trend[701] trend[702] trend[703] trend[704] trend[705] trend[706]
## [1,]  0.4285345  0.4285939  0.4286534  0.4287128  0.4287722  0.4288316
##      trend[707] trend[708] trend[709] trend[710] trend[711] trend[712]
## [1,]  0.4288911  0.4289505  0.4290099  0.4290693  0.4291287  0.4291882
##      trend[713] trend[714] trend[715] trend[716] trend[717] trend[718]
## [1,]  0.4292476   0.429307  0.4293664  0.4294259  0.4294853  0.4295447
##      trend[719] trend[720] trend[721] trend[722] trend[723] trend[724]
## [1,]  0.4296041  0.4296635   0.429723  0.4297824  0.4298418  0.4299012
##      trend[725] trend[726] trend[727] trend[728] trend[729] trend[730]
## [1,]  0.4299607  0.4300201  0.4300795  0.4301389  0.4301984  0.4302578
##      trend[731] trend[732] trend[733] trend[734] trend[735] trend[736]
## [1,]  0.4303172  0.4303766   0.430436  0.4304955  0.4305549  0.4306143
##      trend[737] trend[738] trend[739] trend[740] trend[741] trend[742]
## [1,]  0.4306737  0.4307332  0.4307926   0.430852  0.4309114  0.4309708
##      trend[743] trend[744] trend[745] trend[746] trend[747] trend[748]
## [1,]  0.4310303  0.4310897  0.4311491  0.4312085   0.431268  0.4313274
##      trend[749] trend[750] trend[751] trend[752] trend[753] trend[754]
## [1,]  0.4313868  0.4314462  0.4315057  0.4315651  0.4316245  0.4316839
##      trend[755] trend[756] trend[757] trend[758] trend[759] trend[760]
## [1,]  0.4317433  0.4318028  0.4318622  0.4319216   0.431981  0.4320405
##      trend[761] trend[762] trend[763] trend[764] trend[765] trend[766]
## [1,]  0.4320999  0.4321593  0.4322187  0.4322781  0.4323376   0.432397
##      trend[767] trend[768] trend[769] trend[770] trend[771] trend[772]
## [1,]  0.4324564  0.4325158  0.4325753  0.4326347  0.4326941  0.4327535
##      trend[773] trend[774] trend[775] trend[776] trend[777] trend[778]
## [1,]   0.432813  0.4328724  0.4329318  0.4329912  0.4330506  0.4331101
##      trend[779] trend[780] trend[781] trend[782] trend[783] trend[784]
## [1,]  0.4331695  0.4332289  0.4332883  0.4333478  0.4334072  0.4334666
##      trend[785] trend[786] trend[787] trend[788] trend[789] trend[790]
## [1,]   0.433526  0.4335855  0.4336449  0.4337043  0.4337637  0.4338231
##      trend[791] trend[792] trend[793] trend[794] trend[795] trend[796]
## [1,]  0.4338826   0.433942  0.4340014  0.4340608  0.4341203  0.4341797
##      trend[797] trend[798] trend[799] trend[800] trend[801] trend[802]
## [1,]  0.4342391  0.4342985  0.4343579  0.4344174  0.4344768  0.4345362
##      trend[803] trend[804] trend[805] trend[806] trend[807] trend[808]
## [1,]  0.4345956  0.4346551  0.4347145  0.4347739  0.4348333  0.4348928
##      trend[809] trend[810] trend[811] trend[812] trend[813] trend[814]
## [1,]  0.4349522  0.4350116   0.435071  0.4351304  0.4351899  0.4352493
##      trend[815] trend[816] trend[817] trend[818] trend[819] trend[820]
## [1,]  0.4353087  0.4353681  0.4354276   0.435487  0.4355464  0.4356058
##      trend[821] trend[822] trend[823] trend[824] trend[825] trend[826]
## [1,]  0.4356653  0.4357247  0.4357841  0.4358435  0.4359029  0.4359624
##      trend[827] trend[828] trend[829] trend[830] trend[831] trend[832]
## [1,]  0.4360218  0.4360812  0.4361406  0.4362001  0.4362595  0.4363189
##      trend[833] trend[834] trend[835] trend[836] trend[837] trend[838]
## [1,]  0.4363783  0.4364377  0.4364972  0.4365566   0.436616  0.4366754
##      trend[839] trend[840] trend[841] trend[842] trend[843] trend[844]
## [1,]  0.4367349  0.4367943  0.4368537  0.4369184  0.4369831  0.4370478
##      trend[845] trend[846] trend[847] trend[848] trend[849] trend[850]
## [1,]  0.4371125  0.4371772  0.4372419  0.4373066  0.4373713   0.437436
##      trend[851] trend[852] trend[853] trend[854] trend[855] trend[856]
## [1,]  0.4375007  0.4375654  0.4376301  0.4376948  0.4377595  0.4378242
##      trend[857] trend[858] trend[859] trend[860] trend[861] trend[862]
## [1,]  0.4378888  0.4379535  0.4380182  0.4380829  0.4381476  0.4382123
##      trend[863] trend[864] trend[865] trend[866] trend[867] trend[868]
## [1,]   0.438277  0.4383417  0.4384064  0.4384711  0.4385358  0.4386005
##      trend[869] trend[870] trend[871] trend[872] trend[873] trend[874]
## [1,]  0.4386652  0.4387299  0.4387946  0.4388593   0.438924  0.4389887
##      trend[875] trend[876] trend[877] trend[878] trend[879] trend[880]
## [1,]  0.4390534  0.4391181  0.4391828  0.4392475  0.4393122  0.4393769
##      trend[881] trend[882] trend[883] trend[884] trend[885] trend[886]
## [1,]  0.4394416  0.4395063  0.4395709  0.4396356  0.4397003   0.439765
##      trend[887] trend[888] trend[889] trend[890] trend[891] trend[892]
## [1,]  0.4398297  0.4398944  0.4399615  0.4400286  0.4400956  0.4401627
##      trend[893] trend[894] trend[895] trend[896] trend[897] trend[898]
## [1,]  0.4402298  0.4402969  0.4403639   0.440431  0.4404981  0.4405652
##      trend[899] trend[900] trend[901] trend[902] trend[903] trend[904]
## [1,]  0.4406322  0.4406993  0.4407664  0.4408335  0.4409005  0.4409676
##      trend[905] trend[906] trend[907] trend[908] trend[909] trend[910]
## [1,]  0.4410347  0.4411018  0.4411688  0.4412359   0.441303    0.44137
##      trend[911] trend[912] trend[913] trend[914] trend[915] trend[916]
## [1,]  0.4414371  0.4415042  0.4415713  0.4416383  0.4417054  0.4417725
##      trend[917] trend[918] trend[919] trend[920] trend[921] trend[922]
## [1,]  0.4418396  0.4419066  0.4419737  0.4420408  0.4421079  0.4421749
##      trend[923] trend[924] trend[925] trend[926] trend[927] trend[928]
## [1,]   0.442242  0.4423091  0.4423761  0.4424432  0.4425103  0.4425774
##      trend[929] trend[930] trend[931] trend[932] trend[933] trend[934]
## [1,]  0.4426444  0.4427115  0.4427786  0.4428457  0.4429127  0.4429798
##      trend[935] trend[936] trend[937] trend[938] trend[939] trend[940]
## [1,]  0.4430469   0.443147  0.4432471  0.4433472  0.4434473  0.4435474
##      trend[941] trend[942] trend[943] trend[944] trend[945] trend[946]
## [1,]  0.4436476  0.4437477  0.4438478  0.4439479   0.444048  0.4441481
##      trend[947] trend[948] trend[949] trend[950] trend[951] trend[952]
## [1,]  0.4442482  0.4443483  0.4444484  0.4445486  0.4446487  0.4447488
##      trend[953] trend[954] trend[955] trend[956] trend[957] trend[958]
## [1,]  0.4448489   0.444949  0.4450491  0.4451492  0.4452493  0.4453494
##      trend[959] trend[960] trend[961] trend[962] trend[963] trend[964]
## [1,]  0.4454496  0.4455497  0.4456498  0.4457499    0.44585  0.4459501
##      trend[965] trend[966] trend[967] trend[968] trend[969] trend[970]
## [1,]  0.4460502  0.4461503  0.4462504  0.4463505  0.4464507  0.4465508
##      trend[971] trend[972] trend[973] trend[974] trend[975] trend[976]
## [1,]  0.4466509   0.446751  0.4468511  0.4469512  0.4470513  0.4471514
##      trend[977] trend[978] trend[979] trend[980] trend[981] trend[982]
## [1,]  0.4472515  0.4473517  0.4474518  0.4475519   0.447652  0.4478047
##      trend[983] trend[984] trend[985] trend[986] trend[987] trend[988]
## [1,]  0.4479574  0.4481101  0.4482628  0.4484155  0.4485682   0.448721
##      trend[989] trend[990] trend[991] trend[992] trend[993] trend[994]
## [1,]  0.4488737  0.4490264  0.4491791  0.4493318  0.4494845  0.4496372
##      trend[995] trend[996] trend[997] trend[998] trend[999] trend[1000]
## [1,]  0.4497899  0.4499426  0.4500953   0.450248  0.4504008   0.4505535
##      trend[1001] trend[1002] trend[1003] trend[1004] trend[1005] trend[1006]
## [1,]   0.4507062   0.4508589   0.4510116   0.4511643    0.451317   0.4514697
##      trend[1007] trend[1008] trend[1009] trend[1010] trend[1011] trend[1012]
## [1,]   0.4516224   0.4517751   0.4519278   0.4520806   0.4522333    0.452386
##      trend[1013] trend[1014] trend[1015] trend[1016] trend[1017] trend[1018]
## [1,]   0.4525387   0.4526914   0.4528441   0.4529968   0.4531495   0.4533022
##      trend[1019] trend[1020] trend[1021] trend[1022] trend[1023] trend[1024]
## [1,]   0.4534549   0.4536076   0.4537604   0.4539131   0.4540658   0.4542185
##      trend[1025] trend[1026] trend[1027] trend[1028] trend[1029] trend[1030]
## [1,]   0.4543712   0.4545239   0.4546766   0.4548293   0.4549993   0.4551693
##      trend[1031] trend[1032] trend[1033] trend[1034] trend[1035] trend[1036]
## [1,]   0.4553393   0.4555093   0.4556793   0.4558492   0.4560192   0.4561892
##      trend[1037] trend[1038] trend[1039] trend[1040] trend[1041] trend[1042]
## [1,]   0.4563592   0.4565292   0.4566992   0.4568692   0.4570391   0.4572091
##      trend[1043] trend[1044] trend[1045] trend[1046] trend[1047] trend[1048]
## [1,]   0.4573791   0.4575491   0.4577191   0.4578891   0.4580591   0.4582291
##      trend[1049] trend[1050] trend[1051] trend[1052] trend[1053] trend[1054]
## [1,]    0.458399    0.458569    0.458739    0.458909    0.459079    0.459249
##      trend[1055] trend[1056] trend[1057] trend[1058] trend[1059] trend[1060]
## [1,]    0.459419   0.4595889   0.4597589   0.4599289   0.4600989   0.4602689
##      trend[1061] trend[1062] trend[1063] trend[1064] trend[1065] trend[1066]
## [1,]   0.4604389   0.4606089   0.4607789   0.4609488   0.4611188   0.4612888
##      trend[1067] trend[1068] trend[1069] trend[1070] trend[1071] trend[1072]
## [1,]   0.4614588   0.4616288   0.4617988   0.4619688   0.4621387   0.4623087
##      trend[1073] trend[1074] trend[1075] trend[1076] trend[1077] trend[1078]
## [1,]   0.4624787   0.4626487   0.4628187   0.4629887   0.4631587   0.4633287
##      trend[1079] trend[1080] trend[1081] trend[1082] trend[1083] trend[1084]
## [1,]   0.4634986   0.4636686   0.4638386   0.4640086   0.4641786   0.4643486
##      trend[1085] trend[1086] trend[1087] trend[1088] trend[1089] trend[1090]
## [1,]   0.4645186   0.4646885   0.4648585   0.4650285   0.4651985   0.4653685
##      trend[1091] trend[1092] trend[1093] trend[1094] trend[1095] trend[1096]
## [1,]   0.4655385   0.4657085   0.4658785   0.4660484   0.4662184   0.4663884
##      trend[1097] trend[1098] trend[1099] trend[1100] trend[1101] trend[1102]
## [1,]   0.4665584   0.4667284   0.4668984   0.4670684   0.4672383   0.4674083
##      trend[1103] trend[1104] trend[1105] trend[1106] trend[1107] trend[1108]
## [1,]   0.4675783   0.4677483   0.4679183   0.4680883   0.4682583   0.4684283
##      trend[1109] trend[1110] trend[1111] trend[1112] trend[1113] trend[1114]
## [1,]   0.4685982   0.4687682   0.4689382   0.4691082   0.4692782   0.4694482
##      trend[1115] trend[1116] trend[1117] trend[1118] trend[1119] trend[1120]
## [1,]   0.4696182   0.4697881   0.4699581   0.4701281   0.4702981   0.4704681
##      trend[1121] trend[1122] trend[1123] trend[1124] trend[1125] trend[1126]
## [1,]   0.4706381   0.4708081   0.4709781    0.471148    0.471318    0.471488
##      trend[1127] trend[1128] trend[1129] trend[1130] trend[1131] trend[1132]
## [1,]    0.471658    0.471828    0.471998    0.472168   0.4723379   0.4725079
##      trend[1133] trend[1134] trend[1135] trend[1136] trend[1137] trend[1138]
## [1,]   0.4726779   0.4728479   0.4730179   0.4731879   0.4733579   0.4735279
##      trend[1139] trend[1140] trend[1141] trend[1142] trend[1143] trend[1144]
## [1,]   0.4736978   0.4738678   0.4740378   0.4742078   0.4743778   0.4745478
##      trend[1145] trend[1146] trend[1147] trend[1148] trend[1149] trend[1150]
## [1,]   0.4747178   0.4748877   0.4750577   0.4752277   0.4753977   0.4755677
##      trend[1151] trend[1152] trend[1153] trend[1154] trend[1155] trend[1156]
## [1,]   0.4757377   0.4759077   0.4760777   0.4762476   0.4764176   0.4765876
##      trend[1157] trend[1158] trend[1159] trend[1160] trend[1161] trend[1162]
## [1,]   0.4767576   0.4769276   0.4770976   0.4772676   0.4774375   0.4776075
##      trend[1163] trend[1164] trend[1165] trend[1166] trend[1167] trend[1168]
## [1,]   0.4777775   0.4779475   0.4781175   0.4782875   0.4784575   0.4786275
##      trend[1169] trend[1170] trend[1171] trend[1172] trend[1173] trend[1174]
## [1,]    0.478753   0.4788785   0.4790041   0.4791296   0.4792551   0.4793807
##      trend[1175] trend[1176] trend[1177] trend[1178] trend[1179] trend[1180]
## [1,]   0.4795062   0.4796317   0.4797573   0.4798828   0.4800084   0.4801339
##      trend[1181] trend[1182] trend[1183] trend[1184] trend[1185] trend[1186]
## [1,]   0.4802594    0.480385   0.4805105    0.480636   0.4807616   0.4808871
##      trend[1187] trend[1188] trend[1189] trend[1190] trend[1191] trend[1192]
## [1,]   0.4810126   0.4811382   0.4812637   0.4813892   0.4815148   0.4816403
##      trend[1193] trend[1194] trend[1195] trend[1196] trend[1197] trend[1198]
## [1,]   0.4817659   0.4818914   0.4820169   0.4821425    0.482268   0.4823935
##      trend[1199] trend[1200] trend[1201] trend[1202] trend[1203] trend[1204]
## [1,]   0.4825191   0.4826446   0.4827701   0.4828957   0.4830212   0.4831468
##      trend[1205] trend[1206] trend[1207] trend[1208] trend[1209] trend[1210]
## [1,]   0.4832723   0.4833978   0.4835234   0.4836489   0.4837744      0.4839
##      trend[1211] trend[1212] trend[1213] trend[1214] trend[1215] trend[1216]
## [1,]   0.4840255    0.484151   0.4842766   0.4844021   0.4845277   0.4846532
##      trend[1217] trend[1218] trend[1219] trend[1220] trend[1221] trend[1222]
## [1,]   0.4847787   0.4849043   0.4850298   0.4851553   0.4852809   0.4854064
##      trend[1223] trend[1224] trend[1225] trend[1226] trend[1227] trend[1228]
## [1,]   0.4855319   0.4856575    0.485783   0.4859086   0.4860341   0.4861596
##      trend[1229] trend[1230] trend[1231] trend[1232] trend[1233] trend[1234]
## [1,]   0.4862852   0.4864107   0.4865362   0.4866618   0.4867873   0.4869128
##      trend[1235] trend[1236] trend[1237] trend[1238] trend[1239] trend[1240]
## [1,]   0.4870384   0.4871639   0.4872894    0.487415   0.4875405   0.4876661
##      trend[1241] trend[1242] trend[1243] trend[1244] trend[1245] trend[1246]
## [1,]   0.4877916   0.4879171   0.4880427   0.4881682   0.4882937   0.4884193
##      trend[1247] trend[1248] trend[1249] trend[1250] trend[1251] trend[1252]
## [1,]   0.4885448   0.4886703   0.4887959   0.4889214    0.489047   0.4891725
##      trend[1253] trend[1254] trend[1255] trend[1256] trend[1257] trend[1258]
## [1,]    0.489298   0.4894236   0.4895491   0.4896746   0.4898002   0.4899257
##      trend[1259] trend[1260] trend[1261] trend[1262] trend[1263] trend[1264]
## [1,]   0.4900512   0.4901768   0.4903023   0.4904279   0.4905534   0.4906789
##      trend[1265] trend[1266] trend[1267] trend[1268] trend[1269] trend[1270]
## [1,]   0.4908045     0.49093   0.4910555   0.4911811   0.4913066   0.4914321
##      trend[1271] trend[1272] trend[1273] trend[1274] trend[1275] trend[1276]
## [1,]   0.4915577   0.4916832   0.4918088   0.4919343   0.4920598   0.4921854
##      trend[1277] trend[1278] trend[1279] trend[1280] trend[1281] trend[1282]
## [1,]   0.4923109   0.4924364    0.492562   0.4926875    0.492813   0.4929386
##      trend[1283] trend[1284] trend[1285] trend[1286] trend[1287] trend[1288]
## [1,]   0.4930641   0.4931896   0.4933152   0.4934407   0.4935663   0.4936918
##      trend[1289] trend[1290] trend[1291] trend[1292] trend[1293] trend[1294]
## [1,]   0.4938173   0.4939429   0.4940684   0.4941939   0.4943195    0.494445
##      trend[1295] trend[1296] trend[1297] trend[1298] trend[1299] trend[1300]
## [1,]   0.4945705   0.4946961   0.4948216   0.4949472   0.4950727   0.4951982
##      trend[1301] trend[1302] trend[1303] trend[1304] trend[1305] trend[1306]
## [1,]   0.4953238   0.4954493   0.4955748   0.4957004   0.4958259   0.4959514
##      trend[1307] trend[1308] trend[1309] trend[1310] trend[1311] trend[1312]
## [1,]    0.496077   0.4962025   0.4963281   0.4964536   0.4965791   0.4967047
##      trend[1313] trend[1314] trend[1315] trend[1316] trend[1317] trend[1318]
## [1,]   0.4968302   0.4969557   0.4970813   0.4972068   0.4973323   0.4974579
##      trend[1319] trend[1320] trend[1321] trend[1322] trend[1323] trend[1324]
## [1,]   0.4975834    0.497709   0.4978345     0.49796   0.4980856   0.4982111
##      trend[1325] trend[1326] trend[1327] trend[1328] trend[1329] trend[1330]
## [1,]   0.4983366   0.4984622   0.4985877   0.4987132   0.4988388   0.4989643
##      trend[1331] trend[1332] trend[1333] trend[1334] trend[1335] trend[1336]
## [1,]   0.4990898   0.4992154   0.4993409   0.4994665    0.499592   0.4997175
##      trend[1337] trend[1338] trend[1339] trend[1340] trend[1341] trend[1342]
## [1,]   0.4998431   0.4999686   0.5000941   0.5002197   0.5003452   0.5004707
##      trend[1343] trend[1344] trend[1345] trend[1346] trend[1347] trend[1348]
## [1,]   0.5005963   0.5007218   0.5008474   0.5009729   0.5010984    0.501224
##      trend[1349] trend[1350] trend[1351] trend[1352] trend[1353] trend[1354]
## [1,]   0.5013495    0.501475   0.5016006   0.5017261   0.5018516   0.5019772
##      trend[1355] trend[1356] trend[1357] trend[1358] trend[1359] trend[1360]
## [1,]   0.5021027   0.5022283   0.5023538   0.5024793   0.5026049   0.5027304
##      trend[1361] trend[1362] trend[1363] trend[1364] trend[1365] trend[1366]
## [1,]   0.5028559   0.5029815    0.503107   0.5032325   0.5033581   0.5034836
##      trend[1367] trend[1368] trend[1369] trend[1370] trend[1371] trend[1372]
## [1,]   0.5036092   0.5037347   0.5038602   0.5039858   0.5041113   0.5042368
##      trend[1373] trend[1374] trend[1375] trend[1376] trend[1377] trend[1378]
## [1,]   0.5043624   0.5044879   0.5046134    0.504739   0.5048645     0.50499
##      trend[1379] trend[1380] trend[1381] trend[1382] trend[1383] trend[1384]
## [1,]   0.5051156   0.5052411   0.5053667   0.5054922   0.5056177   0.5057433
##      trend[1385] trend[1386] trend[1387] trend[1388] trend[1389] trend[1390]
## [1,]   0.5058688   0.5059943   0.5061199   0.5062454   0.5063709   0.5064965
##      trend[1391] trend[1392] trend[1393] trend[1394] trend[1395] trend[1396]
## [1,]    0.506622   0.5067476   0.5068731   0.5069986   0.5071242   0.5072497
##      trend[1397] trend[1398] trend[1399] trend[1400] trend[1401] trend[1402]
## [1,]   0.5073752   0.5075008   0.5076263   0.5077518   0.5078774   0.5080029
##      trend[1403] trend[1404] trend[1405] trend[1406] trend[1407] trend[1408]
## [1,]   0.5081285    0.508254   0.5083795   0.5085051   0.5086306   0.5087561
##      trend[1409] trend[1410] trend[1411] trend[1412] trend[1413] trend[1414]
## [1,]   0.5088817   0.5090072   0.5091327   0.5092583   0.5093838   0.5095094
##      trend[1415] trend[1416] trend[1417] trend[1418] trend[1419] trend[1420]
## [1,]   0.5096349   0.5097604    0.509886   0.5100115    0.510137   0.5102626
##      trend[1421] trend[1422] trend[1423] trend[1424] trend[1425] trend[1426]
## [1,]   0.5103881   0.5105136   0.5106392   0.5107647   0.5108902   0.5110158
##      trend[1427] trend[1428] trend[1429] trend[1430] trend[1431] trend[1432]
## [1,]   0.5111413   0.5112669   0.5113924   0.5115179   0.5116435    0.511769
##      trend[1433] trend[1434] trend[1435] trend[1436] trend[1437] trend[1438]
## [1,]   0.5118945   0.5120201   0.5121456   0.5122711   0.5123967   0.5125222
##      trend[1439] trend[1440] trend[1441] trend[1442] trend[1443] trend[1444]
## [1,]   0.5126478   0.5127733   0.5128988   0.5130244   0.5131499   0.5132754
##      trend[1445] trend[1446] trend[1447] trend[1448] trend[1449] trend[1450]
## [1,]    0.513401   0.5135265    0.513652   0.5137776   0.5139031   0.5140287
##      trend[1451] trend[1452] trend[1453] trend[1454] trend[1455] trend[1456]
## [1,]   0.5141542   0.5142797   0.5144053   0.5145308   0.5146563   0.5147819
##      trend[1457] trend[1458] trend[1459] trend[1460] trend[1461]
## [1,]   0.5149074   0.5150329   0.5151585    0.515284   0.5154095
## 
## 
## $params
## $params$k
## [1] -0.3295687
## 
## $params$m
## [1] 0.3550251
## 
## $params$delta
##              [,1]          [,2]      [,3]      [,4]      [,5]          [,6]
## [1,] 1.256203e-07 -2.981828e-08 0.2662971 0.4727642 0.1918457 -1.123155e-07
##              [,7]       [,8]       [,9]        [,10]         [,11]        [,12]
## [1,] 5.084654e-08 -0.2085096 -0.2661333 2.654932e-08 -3.862036e-09 1.096295e-07
##              [,13]       [,14]       [,15]         [,16]        [,17]
## [1,] -4.993257e-09 -0.01140498 -0.02853337 -2.476382e-08 1.702067e-07
##            [,18]       [,19]      [,20]      [,21]     [,22]        [,23]
## [1,] 0.007699039 0.003470921 0.04823478 0.07679313 0.0252252 3.485977e-08
##             [,24]       [,25]
## [1,] 3.816875e-08 -0.06489775
## 
## $params$sigma_obs
## [1] 0.02706113
## 
## $params$beta
##             [,1]       [,2]        [,3]         [,4]        [,5]        [,6]
## [1,] -0.01495432 -0.1393878 -0.02409588 -0.007911498 -0.01775391 -0.02432144
##             [,7]         [,8]        [,9]       [,10]      [,11]       [,12]
## [1,] 0.007720784 -0.008146249 0.006691417 -0.01189065 0.01537089 0.003035046
##            [,13]       [,14]       [,15]       [,16]        [,17]       [,18]
## [1,] 0.003266428 0.009648419 0.004178968 0.005075157 -0.007409245 0.005949041
##             [,19]        [,20]      [,21]        [,22]       [,23]        [,24]
## [1,] -0.004866335 -0.000455657 0.07696754 -0.002570954 -0.04462192 -0.009995636
##           [,25]       [,26]         [,27]      [,28]         [,29]      [,30]
## [1,] 0.04729545 0.006687884 -5.301163e-11 0.03808422 -1.060233e-10 0.03808422
##              [,31]      [,32]         [,33]      [,34]
## [1,] -2.660458e-11 0.03808422 -2.120465e-10 0.03808422
## 
## $params$trend
##    [1] 0.3550251 0.3547994 0.3545736 0.3543479 0.3541222 0.3538964 0.3536707
##    [8] 0.3534450 0.3532192 0.3529935 0.3527678 0.3525420 0.3523163 0.3520906
##   [15] 0.3518649 0.3516391 0.3514134 0.3511877 0.3509619 0.3507362 0.3505105
##   [22] 0.3502847 0.3500590 0.3498333 0.3496075 0.3493818 0.3491561 0.3489303
##   [29] 0.3487046 0.3484789 0.3482531 0.3480274 0.3478017 0.3475759 0.3473502
##   [36] 0.3471245 0.3468987 0.3466730 0.3464473 0.3462216 0.3459958 0.3457701
##   [43] 0.3455444 0.3453186 0.3450929 0.3448672 0.3446414 0.3444157 0.3441900
##   [50] 0.3439642 0.3437385 0.3435128 0.3432870 0.3430613 0.3428356 0.3426098
##   [57] 0.3423841 0.3421584 0.3419326 0.3417069 0.3414812 0.3412555 0.3410297
##   [64] 0.3408040 0.3405783 0.3403525 0.3401268 0.3399011 0.3396753 0.3394496
##   [71] 0.3392239 0.3389981 0.3387724 0.3385467 0.3383209 0.3380952 0.3378695
##   [78] 0.3376437 0.3374180 0.3371923 0.3369665 0.3367408 0.3365151 0.3362893
##   [85] 0.3360636 0.3358379 0.3356122 0.3353864 0.3351607 0.3349350 0.3347092
##   [92] 0.3344835 0.3342578 0.3340320 0.3338063 0.3335806 0.3333548 0.3331291
##   [99] 0.3329034 0.3326776 0.3324519 0.3322262 0.3320004 0.3317747 0.3315490
##  [106] 0.3313232 0.3310975 0.3308718 0.3306461 0.3304203 0.3301946 0.3299689
##  [113] 0.3297431 0.3295174 0.3292917 0.3290659 0.3288402 0.3286145 0.3283887
##  [120] 0.3281630 0.3279373 0.3277115 0.3274858 0.3272601 0.3270343 0.3268086
##  [127] 0.3265829 0.3263571 0.3261314 0.3259057 0.3256799 0.3254542 0.3252285
##  [134] 0.3250028 0.3247770 0.3245513 0.3243256 0.3240998 0.3238741 0.3236484
##  [141] 0.3234226 0.3233793 0.3233360 0.3232926 0.3232493 0.3232059 0.3231626
##  [148] 0.3231193 0.3230759 0.3230326 0.3229893 0.3229459 0.3229026 0.3228593
##  [155] 0.3228159 0.3227726 0.3227292 0.3226859 0.3226426 0.3225992 0.3225559
##  [162] 0.3225126 0.3224692 0.3224259 0.3223826 0.3223392 0.3222959 0.3222525
##  [169] 0.3222092 0.3221659 0.3221225 0.3220792 0.3220359 0.3219925 0.3219492
##  [176] 0.3219058 0.3218625 0.3218192 0.3217758 0.3217325 0.3216892 0.3216458
##  [183] 0.3216025 0.3215592 0.3215158 0.3214725 0.3214291 0.3213858 0.3216663
##  [190] 0.3219468 0.3222272 0.3225077 0.3227882 0.3230687 0.3233491 0.3236296
##  [197] 0.3239101 0.3241906 0.3244710 0.3247515 0.3250320 0.3253125 0.3255929
##  [204] 0.3258734 0.3261539 0.3264343 0.3267148 0.3269953 0.3272758 0.3275562
##  [211] 0.3278367 0.3281172 0.3283977 0.3286781 0.3289586 0.3292391 0.3295196
##  [218] 0.3298000 0.3300805 0.3303610 0.3306415 0.3309219 0.3312024 0.3314829
##  [225] 0.3317634 0.3320438 0.3323243 0.3326048 0.3328853 0.3331657 0.3334462
##  [232] 0.3337267 0.3340072 0.3342876 0.3346995 0.3351114 0.3355233 0.3359351
##  [239] 0.3363470 0.3367589 0.3371708 0.3375826 0.3379945 0.3384064 0.3388183
##  [246] 0.3392301 0.3396420 0.3400539 0.3404658 0.3408776 0.3412895 0.3417014
##  [253] 0.3421133 0.3425251 0.3429370 0.3433489 0.3437608 0.3441726 0.3445845
##  [260] 0.3449964 0.3454083 0.3458201 0.3462320 0.3466439 0.3470558 0.3474677
##  [267] 0.3478795 0.3482914 0.3487033 0.3491152 0.3495270 0.3499389 0.3503508
##  [274] 0.3507627 0.3511745 0.3515864 0.3519983 0.3524102 0.3528220 0.3532339
##  [281] 0.3536458 0.3540577 0.3544695 0.3548814 0.3552933 0.3557052 0.3561170
##  [288] 0.3565289 0.3569408 0.3573527 0.3577645 0.3581764 0.3585883 0.3590002
##  [295] 0.3594120 0.3598239 0.3602358 0.3606477 0.3610595 0.3614714 0.3618833
##  [302] 0.3622952 0.3627070 0.3631189 0.3635308 0.3639427 0.3643546 0.3647664
##  [309] 0.3651783 0.3655902 0.3660021 0.3664139 0.3668258 0.3672377 0.3676496
##  [316] 0.3680614 0.3684733 0.3688852 0.3692971 0.3697089 0.3701208 0.3705327
##  [323] 0.3709446 0.3713564 0.3717683 0.3721802 0.3725921 0.3730039 0.3734158
##  [330] 0.3738277 0.3742396 0.3746514 0.3750633 0.3754752 0.3758871 0.3762989
##  [337] 0.3767108 0.3771227 0.3775346 0.3779464 0.3783583 0.3787702 0.3791821
##  [344] 0.3795939 0.3800058 0.3804177 0.3808296 0.3812414 0.3816533 0.3820652
##  [351] 0.3824771 0.3828890 0.3833008 0.3837127 0.3841246 0.3845365 0.3849483
##  [358] 0.3853602 0.3857721 0.3861840 0.3865958 0.3870077 0.3874196 0.3878315
##  [365] 0.3882433 0.3886552 0.3890671 0.3894790 0.3898908 0.3903027 0.3907146
##  [372] 0.3911265 0.3915383 0.3919502 0.3922193 0.3924883 0.3927574 0.3930265
##  [379] 0.3932955 0.3935646 0.3938336 0.3941027 0.3943718 0.3946408 0.3949099
##  [386] 0.3951789 0.3954480 0.3957171 0.3959861 0.3962552 0.3965242 0.3967933
##  [393] 0.3970624 0.3973314 0.3976005 0.3978696 0.3981386 0.3984077 0.3986767
##  [400] 0.3989458 0.3992149 0.3994839 0.3997530 0.4000220 0.4002911 0.4005602
##  [407] 0.4008292 0.4010983 0.4013673 0.4016364 0.4019055 0.4021745 0.4024436
##  [414] 0.4027126 0.4029817 0.4032508 0.4035198 0.4037889 0.4040580 0.4043270
##  [421] 0.4045961 0.4046829 0.4047696 0.4048564 0.4049432 0.4050300 0.4051167
##  [428] 0.4052035 0.4052903 0.4053771 0.4054638 0.4055506 0.4056374 0.4057242
##  [435] 0.4058110 0.4058977 0.4059845 0.4060713 0.4061581 0.4062448 0.4063316
##  [442] 0.4064184 0.4065052 0.4065920 0.4066787 0.4067655 0.4068523 0.4069391
##  [449] 0.4070258 0.4071126 0.4071994 0.4072862 0.4073730 0.4074597 0.4075465
##  [456] 0.4076333 0.4077201 0.4078068 0.4078936 0.4079804 0.4080672 0.4081540
##  [463] 0.4082407 0.4083275 0.4084143 0.4085011 0.4085878 0.4086746 0.4087614
##  [470] 0.4088482 0.4089350 0.4090217 0.4091085 0.4091953 0.4092821 0.4093688
##  [477] 0.4094556 0.4095424 0.4096292 0.4097160 0.4098027 0.4098895 0.4099763
##  [484] 0.4100631 0.4101498 0.4102366 0.4103234 0.4104102 0.4104970 0.4105837
##  [491] 0.4106705 0.4107573 0.4108441 0.4109308 0.4110176 0.4111044 0.4111912
##  [498] 0.4112780 0.4113647 0.4114515 0.4115383 0.4116251 0.4117118 0.4117986
##  [505] 0.4118854 0.4119722 0.4120590 0.4121457 0.4122325 0.4123193 0.4124061
##  [512] 0.4124928 0.4125796 0.4126664 0.4127532 0.4128400 0.4129267 0.4130135
##  [519] 0.4131003 0.4131871 0.4132738 0.4133606 0.4134474 0.4135342 0.4136210
##  [526] 0.4137077 0.4137945 0.4138813 0.4139681 0.4140548 0.4141416 0.4142284
##  [533] 0.4143152 0.4144020 0.4144887 0.4145755 0.4146623 0.4147491 0.4148358
##  [540] 0.4149226 0.4150094 0.4150962 0.4151830 0.4152697 0.4153565 0.4154433
##  [547] 0.4155301 0.4156168 0.4157036 0.4157904 0.4158772 0.4159640 0.4160507
##  [554] 0.4161375 0.4162243 0.4163111 0.4163978 0.4164846 0.4165714 0.4166582
##  [561] 0.4167450 0.4168317 0.4169185 0.4170053 0.4170921 0.4171788 0.4172656
##  [568] 0.4173524 0.4174392 0.4175260 0.4176127 0.4176995 0.4177863 0.4178731
##  [575] 0.4179598 0.4180466 0.4181334 0.4182202 0.4183070 0.4183937 0.4184805
##  [582] 0.4185673 0.4186541 0.4187408 0.4188276 0.4189144 0.4190012 0.4190880
##  [589] 0.4191747 0.4192615 0.4193483 0.4194351 0.4195218 0.4196086 0.4196954
##  [596] 0.4197822 0.4198690 0.4199557 0.4200425 0.4201293 0.4202161 0.4203028
##  [603] 0.4203896 0.4204764 0.4205632 0.4206500 0.4207367 0.4208235 0.4209103
##  [610] 0.4209971 0.4210838 0.4211706 0.4212574 0.4213442 0.4214310 0.4215177
##  [617] 0.4216045 0.4216913 0.4217781 0.4218648 0.4219516 0.4220384 0.4221252
##  [624] 0.4222120 0.4222987 0.4223855 0.4224723 0.4225591 0.4226458 0.4227326
##  [631] 0.4228194 0.4229062 0.4229930 0.4230797 0.4231665 0.4232533 0.4233401
##  [638] 0.4234268 0.4235136 0.4236004 0.4236872 0.4237740 0.4238607 0.4239475
##  [645] 0.4240343 0.4241211 0.4242078 0.4242946 0.4243814 0.4244682 0.4245550
##  [652] 0.4246417 0.4247285 0.4248153 0.4249021 0.4249810 0.4250600 0.4251390
##  [659] 0.4252179 0.4252969 0.4253759 0.4254548 0.4255338 0.4256128 0.4256917
##  [666] 0.4257707 0.4258497 0.4259286 0.4260076 0.4260866 0.4261655 0.4262445
##  [673] 0.4263235 0.4264024 0.4264814 0.4265604 0.4266393 0.4267183 0.4267973
##  [680] 0.4268762 0.4269552 0.4270342 0.4271131 0.4271921 0.4272711 0.4273500
##  [687] 0.4274290 0.4275080 0.4275869 0.4276659 0.4277449 0.4278238 0.4279028
##  [694] 0.4279818 0.4280607 0.4281397 0.4282187 0.4282976 0.4283766 0.4284555
##  [701] 0.4285345 0.4285939 0.4286534 0.4287128 0.4287722 0.4288316 0.4288911
##  [708] 0.4289505 0.4290099 0.4290693 0.4291287 0.4291882 0.4292476 0.4293070
##  [715] 0.4293664 0.4294259 0.4294853 0.4295447 0.4296041 0.4296635 0.4297230
##  [722] 0.4297824 0.4298418 0.4299012 0.4299607 0.4300201 0.4300795 0.4301389
##  [729] 0.4301984 0.4302578 0.4303172 0.4303766 0.4304360 0.4304955 0.4305549
##  [736] 0.4306143 0.4306737 0.4307332 0.4307926 0.4308520 0.4309114 0.4309708
##  [743] 0.4310303 0.4310897 0.4311491 0.4312085 0.4312680 0.4313274 0.4313868
##  [750] 0.4314462 0.4315057 0.4315651 0.4316245 0.4316839 0.4317433 0.4318028
##  [757] 0.4318622 0.4319216 0.4319810 0.4320405 0.4320999 0.4321593 0.4322187
##  [764] 0.4322781 0.4323376 0.4323970 0.4324564 0.4325158 0.4325753 0.4326347
##  [771] 0.4326941 0.4327535 0.4328130 0.4328724 0.4329318 0.4329912 0.4330506
##  [778] 0.4331101 0.4331695 0.4332289 0.4332883 0.4333478 0.4334072 0.4334666
##  [785] 0.4335260 0.4335855 0.4336449 0.4337043 0.4337637 0.4338231 0.4338826
##  [792] 0.4339420 0.4340014 0.4340608 0.4341203 0.4341797 0.4342391 0.4342985
##  [799] 0.4343579 0.4344174 0.4344768 0.4345362 0.4345956 0.4346551 0.4347145
##  [806] 0.4347739 0.4348333 0.4348928 0.4349522 0.4350116 0.4350710 0.4351304
##  [813] 0.4351899 0.4352493 0.4353087 0.4353681 0.4354276 0.4354870 0.4355464
##  [820] 0.4356058 0.4356653 0.4357247 0.4357841 0.4358435 0.4359029 0.4359624
##  [827] 0.4360218 0.4360812 0.4361406 0.4362001 0.4362595 0.4363189 0.4363783
##  [834] 0.4364377 0.4364972 0.4365566 0.4366160 0.4366754 0.4367349 0.4367943
##  [841] 0.4368537 0.4369184 0.4369831 0.4370478 0.4371125 0.4371772 0.4372419
##  [848] 0.4373066 0.4373713 0.4374360 0.4375007 0.4375654 0.4376301 0.4376948
##  [855] 0.4377595 0.4378242 0.4378888 0.4379535 0.4380182 0.4380829 0.4381476
##  [862] 0.4382123 0.4382770 0.4383417 0.4384064 0.4384711 0.4385358 0.4386005
##  [869] 0.4386652 0.4387299 0.4387946 0.4388593 0.4389240 0.4389887 0.4390534
##  [876] 0.4391181 0.4391828 0.4392475 0.4393122 0.4393769 0.4394416 0.4395063
##  [883] 0.4395709 0.4396356 0.4397003 0.4397650 0.4398297 0.4398944 0.4399615
##  [890] 0.4400286 0.4400956 0.4401627 0.4402298 0.4402969 0.4403639 0.4404310
##  [897] 0.4404981 0.4405652 0.4406322 0.4406993 0.4407664 0.4408335 0.4409005
##  [904] 0.4409676 0.4410347 0.4411018 0.4411688 0.4412359 0.4413030 0.4413700
##  [911] 0.4414371 0.4415042 0.4415713 0.4416383 0.4417054 0.4417725 0.4418396
##  [918] 0.4419066 0.4419737 0.4420408 0.4421079 0.4421749 0.4422420 0.4423091
##  [925] 0.4423761 0.4424432 0.4425103 0.4425774 0.4426444 0.4427115 0.4427786
##  [932] 0.4428457 0.4429127 0.4429798 0.4430469 0.4431470 0.4432471 0.4433472
##  [939] 0.4434473 0.4435474 0.4436476 0.4437477 0.4438478 0.4439479 0.4440480
##  [946] 0.4441481 0.4442482 0.4443483 0.4444484 0.4445486 0.4446487 0.4447488
##  [953] 0.4448489 0.4449490 0.4450491 0.4451492 0.4452493 0.4453494 0.4454496
##  [960] 0.4455497 0.4456498 0.4457499 0.4458500 0.4459501 0.4460502 0.4461503
##  [967] 0.4462504 0.4463505 0.4464507 0.4465508 0.4466509 0.4467510 0.4468511
##  [974] 0.4469512 0.4470513 0.4471514 0.4472515 0.4473517 0.4474518 0.4475519
##  [981] 0.4476520 0.4478047 0.4479574 0.4481101 0.4482628 0.4484155 0.4485682
##  [988] 0.4487210 0.4488737 0.4490264 0.4491791 0.4493318 0.4494845 0.4496372
##  [995] 0.4497899 0.4499426 0.4500953 0.4502480 0.4504008 0.4505535 0.4507062
## [1002] 0.4508589 0.4510116 0.4511643 0.4513170 0.4514697 0.4516224 0.4517751
## [1009] 0.4519278 0.4520806 0.4522333 0.4523860 0.4525387 0.4526914 0.4528441
## [1016] 0.4529968 0.4531495 0.4533022 0.4534549 0.4536076 0.4537604 0.4539131
## [1023] 0.4540658 0.4542185 0.4543712 0.4545239 0.4546766 0.4548293 0.4549993
## [1030] 0.4551693 0.4553393 0.4555093 0.4556793 0.4558492 0.4560192 0.4561892
## [1037] 0.4563592 0.4565292 0.4566992 0.4568692 0.4570391 0.4572091 0.4573791
## [1044] 0.4575491 0.4577191 0.4578891 0.4580591 0.4582291 0.4583990 0.4585690
## [1051] 0.4587390 0.4589090 0.4590790 0.4592490 0.4594190 0.4595889 0.4597589
## [1058] 0.4599289 0.4600989 0.4602689 0.4604389 0.4606089 0.4607789 0.4609488
## [1065] 0.4611188 0.4612888 0.4614588 0.4616288 0.4617988 0.4619688 0.4621387
## [1072] 0.4623087 0.4624787 0.4626487 0.4628187 0.4629887 0.4631587 0.4633287
## [1079] 0.4634986 0.4636686 0.4638386 0.4640086 0.4641786 0.4643486 0.4645186
## [1086] 0.4646885 0.4648585 0.4650285 0.4651985 0.4653685 0.4655385 0.4657085
## [1093] 0.4658785 0.4660484 0.4662184 0.4663884 0.4665584 0.4667284 0.4668984
## [1100] 0.4670684 0.4672383 0.4674083 0.4675783 0.4677483 0.4679183 0.4680883
## [1107] 0.4682583 0.4684283 0.4685982 0.4687682 0.4689382 0.4691082 0.4692782
## [1114] 0.4694482 0.4696182 0.4697881 0.4699581 0.4701281 0.4702981 0.4704681
## [1121] 0.4706381 0.4708081 0.4709781 0.4711480 0.4713180 0.4714880 0.4716580
## [1128] 0.4718280 0.4719980 0.4721680 0.4723379 0.4725079 0.4726779 0.4728479
## [1135] 0.4730179 0.4731879 0.4733579 0.4735279 0.4736978 0.4738678 0.4740378
## [1142] 0.4742078 0.4743778 0.4745478 0.4747178 0.4748877 0.4750577 0.4752277
## [1149] 0.4753977 0.4755677 0.4757377 0.4759077 0.4760777 0.4762476 0.4764176
## [1156] 0.4765876 0.4767576 0.4769276 0.4770976 0.4772676 0.4774375 0.4776075
## [1163] 0.4777775 0.4779475 0.4781175 0.4782875 0.4784575 0.4786275 0.4787530
## [1170] 0.4788785 0.4790041 0.4791296 0.4792551 0.4793807 0.4795062 0.4796317
## [1177] 0.4797573 0.4798828 0.4800084 0.4801339 0.4802594 0.4803850 0.4805105
## [1184] 0.4806360 0.4807616 0.4808871 0.4810126 0.4811382 0.4812637 0.4813892
## [1191] 0.4815148 0.4816403 0.4817659 0.4818914 0.4820169 0.4821425 0.4822680
## [1198] 0.4823935 0.4825191 0.4826446 0.4827701 0.4828957 0.4830212 0.4831468
## [1205] 0.4832723 0.4833978 0.4835234 0.4836489 0.4837744 0.4839000 0.4840255
## [1212] 0.4841510 0.4842766 0.4844021 0.4845277 0.4846532 0.4847787 0.4849043
## [1219] 0.4850298 0.4851553 0.4852809 0.4854064 0.4855319 0.4856575 0.4857830
## [1226] 0.4859086 0.4860341 0.4861596 0.4862852 0.4864107 0.4865362 0.4866618
## [1233] 0.4867873 0.4869128 0.4870384 0.4871639 0.4872894 0.4874150 0.4875405
## [1240] 0.4876661 0.4877916 0.4879171 0.4880427 0.4881682 0.4882937 0.4884193
## [1247] 0.4885448 0.4886703 0.4887959 0.4889214 0.4890470 0.4891725 0.4892980
## [1254] 0.4894236 0.4895491 0.4896746 0.4898002 0.4899257 0.4900512 0.4901768
## [1261] 0.4903023 0.4904279 0.4905534 0.4906789 0.4908045 0.4909300 0.4910555
## [1268] 0.4911811 0.4913066 0.4914321 0.4915577 0.4916832 0.4918088 0.4919343
## [1275] 0.4920598 0.4921854 0.4923109 0.4924364 0.4925620 0.4926875 0.4928130
## [1282] 0.4929386 0.4930641 0.4931896 0.4933152 0.4934407 0.4935663 0.4936918
## [1289] 0.4938173 0.4939429 0.4940684 0.4941939 0.4943195 0.4944450 0.4945705
## [1296] 0.4946961 0.4948216 0.4949472 0.4950727 0.4951982 0.4953238 0.4954493
## [1303] 0.4955748 0.4957004 0.4958259 0.4959514 0.4960770 0.4962025 0.4963281
## [1310] 0.4964536 0.4965791 0.4967047 0.4968302 0.4969557 0.4970813 0.4972068
## [1317] 0.4973323 0.4974579 0.4975834 0.4977090 0.4978345 0.4979600 0.4980856
## [1324] 0.4982111 0.4983366 0.4984622 0.4985877 0.4987132 0.4988388 0.4989643
## [1331] 0.4990898 0.4992154 0.4993409 0.4994665 0.4995920 0.4997175 0.4998431
## [1338] 0.4999686 0.5000941 0.5002197 0.5003452 0.5004707 0.5005963 0.5007218
## [1345] 0.5008474 0.5009729 0.5010984 0.5012240 0.5013495 0.5014750 0.5016006
## [1352] 0.5017261 0.5018516 0.5019772 0.5021027 0.5022283 0.5023538 0.5024793
## [1359] 0.5026049 0.5027304 0.5028559 0.5029815 0.5031070 0.5032325 0.5033581
## [1366] 0.5034836 0.5036092 0.5037347 0.5038602 0.5039858 0.5041113 0.5042368
## [1373] 0.5043624 0.5044879 0.5046134 0.5047390 0.5048645 0.5049900 0.5051156
## [1380] 0.5052411 0.5053667 0.5054922 0.5056177 0.5057433 0.5058688 0.5059943
## [1387] 0.5061199 0.5062454 0.5063709 0.5064965 0.5066220 0.5067476 0.5068731
## [1394] 0.5069986 0.5071242 0.5072497 0.5073752 0.5075008 0.5076263 0.5077518
## [1401] 0.5078774 0.5080029 0.5081285 0.5082540 0.5083795 0.5085051 0.5086306
## [1408] 0.5087561 0.5088817 0.5090072 0.5091327 0.5092583 0.5093838 0.5095094
## [1415] 0.5096349 0.5097604 0.5098860 0.5100115 0.5101370 0.5102626 0.5103881
## [1422] 0.5105136 0.5106392 0.5107647 0.5108902 0.5110158 0.5111413 0.5112669
## [1429] 0.5113924 0.5115179 0.5116435 0.5117690 0.5118945 0.5120201 0.5121456
## [1436] 0.5122711 0.5123967 0.5125222 0.5126478 0.5127733 0.5128988 0.5130244
## [1443] 0.5131499 0.5132754 0.5134010 0.5135265 0.5136520 0.5137776 0.5139031
## [1450] 0.5140287 0.5141542 0.5142797 0.5144053 0.5145308 0.5146563 0.5147819
## [1457] 0.5149074 0.5150329 0.5151585 0.5152840 0.5154095
## 
## 
## $history
## # A tibble: 1,461 x 5
##    ds                      y floor        t y_scaled
##    <dttm>              <dbl> <dbl>    <dbl>    <dbl>
##  1 2013-01-01 00:00:00  1588     0 0           0.317
##  2 2013-01-02 00:00:00  1538     0 0.000685    0.307
##  3 2013-01-03 00:00:00  1635     0 0.00137     0.327
##  4 2013-01-04 00:00:00  1741     0 0.00205     0.348
##  5 2013-01-05 00:00:00  1887     0 0.00274     0.377
##  6 2013-01-06 00:00:00  1956     0 0.00342     0.391
##  7 2013-01-07 00:00:00  1313     0 0.00411     0.262
##  8 2013-01-08 00:00:00  1538     0 0.00479     0.307
##  9 2013-01-09 00:00:00  1633     0 0.00548     0.326
## 10 2013-01-10 00:00:00  1677     0 0.00616     0.335
## # ... with 1,451 more rows
## 
## $history.dates
##    [1] "2013-01-01 GMT" "2013-01-02 GMT" "2013-01-03 GMT" "2013-01-04 GMT"
##    [5] "2013-01-05 GMT" "2013-01-06 GMT" "2013-01-07 GMT" "2013-01-08 GMT"
##    [9] "2013-01-09 GMT" "2013-01-10 GMT" "2013-01-11 GMT" "2013-01-12 GMT"
##   [13] "2013-01-13 GMT" "2013-01-14 GMT" "2013-01-15 GMT" "2013-01-16 GMT"
##   [17] "2013-01-17 GMT" "2013-01-18 GMT" "2013-01-19 GMT" "2013-01-20 GMT"
##   [21] "2013-01-21 GMT" "2013-01-22 GMT" "2013-01-23 GMT" "2013-01-24 GMT"
##   [25] "2013-01-25 GMT" "2013-01-26 GMT" "2013-01-27 GMT" "2013-01-28 GMT"
##   [29] "2013-01-29 GMT" "2013-01-30 GMT" "2013-01-31 GMT" "2013-02-01 GMT"
##   [33] "2013-02-02 GMT" "2013-02-03 GMT" "2013-02-04 GMT" "2013-02-05 GMT"
##   [37] "2013-02-06 GMT" "2013-02-07 GMT" "2013-02-08 GMT" "2013-02-09 GMT"
##   [41] "2013-02-10 GMT" "2013-02-11 GMT" "2013-02-12 GMT" "2013-02-13 GMT"
##   [45] "2013-02-14 GMT" "2013-02-15 GMT" "2013-02-16 GMT" "2013-02-17 GMT"
##   [49] "2013-02-18 GMT" "2013-02-19 GMT" "2013-02-20 GMT" "2013-02-21 GMT"
##   [53] "2013-02-22 GMT" "2013-02-23 GMT" "2013-02-24 GMT" "2013-02-25 GMT"
##   [57] "2013-02-26 GMT" "2013-02-27 GMT" "2013-02-28 GMT" "2013-03-01 GMT"
##   [61] "2013-03-02 GMT" "2013-03-03 GMT" "2013-03-04 GMT" "2013-03-05 GMT"
##   [65] "2013-03-06 GMT" "2013-03-07 GMT" "2013-03-08 GMT" "2013-03-09 GMT"
##   [69] "2013-03-10 GMT" "2013-03-11 GMT" "2013-03-12 GMT" "2013-03-13 GMT"
##   [73] "2013-03-14 GMT" "2013-03-15 GMT" "2013-03-16 GMT" "2013-03-17 GMT"
##   [77] "2013-03-18 GMT" "2013-03-19 GMT" "2013-03-20 GMT" "2013-03-21 GMT"
##   [81] "2013-03-22 GMT" "2013-03-23 GMT" "2013-03-24 GMT" "2013-03-25 GMT"
##   [85] "2013-03-26 GMT" "2013-03-27 GMT" "2013-03-28 GMT" "2013-03-29 GMT"
##   [89] "2013-03-30 GMT" "2013-03-31 GMT" "2013-04-01 GMT" "2013-04-02 GMT"
##   [93] "2013-04-03 GMT" "2013-04-04 GMT" "2013-04-05 GMT" "2013-04-06 GMT"
##   [97] "2013-04-07 GMT" "2013-04-08 GMT" "2013-04-09 GMT" "2013-04-10 GMT"
##  [101] "2013-04-11 GMT" "2013-04-12 GMT" "2013-04-13 GMT" "2013-04-14 GMT"
##  [105] "2013-04-15 GMT" "2013-04-16 GMT" "2013-04-17 GMT" "2013-04-18 GMT"
##  [109] "2013-04-19 GMT" "2013-04-20 GMT" "2013-04-21 GMT" "2013-04-22 GMT"
##  [113] "2013-04-23 GMT" "2013-04-24 GMT" "2013-04-25 GMT" "2013-04-26 GMT"
##  [117] "2013-04-27 GMT" "2013-04-28 GMT" "2013-04-29 GMT" "2013-04-30 GMT"
##  [121] "2013-05-01 GMT" "2013-05-02 GMT" "2013-05-03 GMT" "2013-05-04 GMT"
##  [125] "2013-05-05 GMT" "2013-05-06 GMT" "2013-05-07 GMT" "2013-05-08 GMT"
##  [129] "2013-05-09 GMT" "2013-05-10 GMT" "2013-05-11 GMT" "2013-05-12 GMT"
##  [133] "2013-05-13 GMT" "2013-05-14 GMT" "2013-05-15 GMT" "2013-05-16 GMT"
##  [137] "2013-05-17 GMT" "2013-05-18 GMT" "2013-05-19 GMT" "2013-05-20 GMT"
##  [141] "2013-05-21 GMT" "2013-05-22 GMT" "2013-05-23 GMT" "2013-05-24 GMT"
##  [145] "2013-05-25 GMT" "2013-05-26 GMT" "2013-05-27 GMT" "2013-05-28 GMT"
##  [149] "2013-05-29 GMT" "2013-05-30 GMT" "2013-05-31 GMT" "2013-06-01 GMT"
##  [153] "2013-06-02 GMT" "2013-06-03 GMT" "2013-06-04 GMT" "2013-06-05 GMT"
##  [157] "2013-06-06 GMT" "2013-06-07 GMT" "2013-06-08 GMT" "2013-06-09 GMT"
##  [161] "2013-06-10 GMT" "2013-06-11 GMT" "2013-06-12 GMT" "2013-06-13 GMT"
##  [165] "2013-06-14 GMT" "2013-06-15 GMT" "2013-06-16 GMT" "2013-06-17 GMT"
##  [169] "2013-06-18 GMT" "2013-06-19 GMT" "2013-06-20 GMT" "2013-06-21 GMT"
##  [173] "2013-06-22 GMT" "2013-06-23 GMT" "2013-06-24 GMT" "2013-06-25 GMT"
##  [177] "2013-06-26 GMT" "2013-06-27 GMT" "2013-06-28 GMT" "2013-06-29 GMT"
##  [181] "2013-06-30 GMT" "2013-07-01 GMT" "2013-07-02 GMT" "2013-07-03 GMT"
##  [185] "2013-07-04 GMT" "2013-07-05 GMT" "2013-07-06 GMT" "2013-07-07 GMT"
##  [189] "2013-07-08 GMT" "2013-07-09 GMT" "2013-07-10 GMT" "2013-07-11 GMT"
##  [193] "2013-07-12 GMT" "2013-07-13 GMT" "2013-07-14 GMT" "2013-07-15 GMT"
##  [197] "2013-07-16 GMT" "2013-07-17 GMT" "2013-07-18 GMT" "2013-07-19 GMT"
##  [201] "2013-07-20 GMT" "2013-07-21 GMT" "2013-07-22 GMT" "2013-07-23 GMT"
##  [205] "2013-07-24 GMT" "2013-07-25 GMT" "2013-07-26 GMT" "2013-07-27 GMT"
##  [209] "2013-07-28 GMT" "2013-07-29 GMT" "2013-07-30 GMT" "2013-07-31 GMT"
##  [213] "2013-08-01 GMT" "2013-08-02 GMT" "2013-08-03 GMT" "2013-08-04 GMT"
##  [217] "2013-08-05 GMT" "2013-08-06 GMT" "2013-08-07 GMT" "2013-08-08 GMT"
##  [221] "2013-08-09 GMT" "2013-08-10 GMT" "2013-08-11 GMT" "2013-08-12 GMT"
##  [225] "2013-08-13 GMT" "2013-08-14 GMT" "2013-08-15 GMT" "2013-08-16 GMT"
##  [229] "2013-08-17 GMT" "2013-08-18 GMT" "2013-08-19 GMT" "2013-08-20 GMT"
##  [233] "2013-08-21 GMT" "2013-08-22 GMT" "2013-08-23 GMT" "2013-08-24 GMT"
##  [237] "2013-08-25 GMT" "2013-08-26 GMT" "2013-08-27 GMT" "2013-08-28 GMT"
##  [241] "2013-08-29 GMT" "2013-08-30 GMT" "2013-08-31 GMT" "2013-09-01 GMT"
##  [245] "2013-09-02 GMT" "2013-09-03 GMT" "2013-09-04 GMT" "2013-09-05 GMT"
##  [249] "2013-09-06 GMT" "2013-09-07 GMT" "2013-09-08 GMT" "2013-09-09 GMT"
##  [253] "2013-09-10 GMT" "2013-09-11 GMT" "2013-09-12 GMT" "2013-09-13 GMT"
##  [257] "2013-09-14 GMT" "2013-09-15 GMT" "2013-09-16 GMT" "2013-09-17 GMT"
##  [261] "2013-09-18 GMT" "2013-09-19 GMT" "2013-09-20 GMT" "2013-09-21 GMT"
##  [265] "2013-09-22 GMT" "2013-09-23 GMT" "2013-09-24 GMT" "2013-09-25 GMT"
##  [269] "2013-09-26 GMT" "2013-09-27 GMT" "2013-09-28 GMT" "2013-09-29 GMT"
##  [273] "2013-09-30 GMT" "2013-10-01 GMT" "2013-10-02 GMT" "2013-10-03 GMT"
##  [277] "2013-10-04 GMT" "2013-10-05 GMT" "2013-10-06 GMT" "2013-10-07 GMT"
##  [281] "2013-10-08 GMT" "2013-10-09 GMT" "2013-10-10 GMT" "2013-10-11 GMT"
##  [285] "2013-10-12 GMT" "2013-10-13 GMT" "2013-10-14 GMT" "2013-10-15 GMT"
##  [289] "2013-10-16 GMT" "2013-10-17 GMT" "2013-10-18 GMT" "2013-10-19 GMT"
##  [293] "2013-10-20 GMT" "2013-10-21 GMT" "2013-10-22 GMT" "2013-10-23 GMT"
##  [297] "2013-10-24 GMT" "2013-10-25 GMT" "2013-10-26 GMT" "2013-10-27 GMT"
##  [301] "2013-10-28 GMT" "2013-10-29 GMT" "2013-10-30 GMT" "2013-10-31 GMT"
##  [305] "2013-11-01 GMT" "2013-11-02 GMT" "2013-11-03 GMT" "2013-11-04 GMT"
##  [309] "2013-11-05 GMT" "2013-11-06 GMT" "2013-11-07 GMT" "2013-11-08 GMT"
##  [313] "2013-11-09 GMT" "2013-11-10 GMT" "2013-11-11 GMT" "2013-11-12 GMT"
##  [317] "2013-11-13 GMT" "2013-11-14 GMT" "2013-11-15 GMT" "2013-11-16 GMT"
##  [321] "2013-11-17 GMT" "2013-11-18 GMT" "2013-11-19 GMT" "2013-11-20 GMT"
##  [325] "2013-11-21 GMT" "2013-11-22 GMT" "2013-11-23 GMT" "2013-11-24 GMT"
##  [329] "2013-11-25 GMT" "2013-11-26 GMT" "2013-11-27 GMT" "2013-11-28 GMT"
##  [333] "2013-11-29 GMT" "2013-11-30 GMT" "2013-12-01 GMT" "2013-12-02 GMT"
##  [337] "2013-12-03 GMT" "2013-12-04 GMT" "2013-12-05 GMT" "2013-12-06 GMT"
##  [341] "2013-12-07 GMT" "2013-12-08 GMT" "2013-12-09 GMT" "2013-12-10 GMT"
##  [345] "2013-12-11 GMT" "2013-12-12 GMT" "2013-12-13 GMT" "2013-12-14 GMT"
##  [349] "2013-12-15 GMT" "2013-12-16 GMT" "2013-12-17 GMT" "2013-12-18 GMT"
##  [353] "2013-12-19 GMT" "2013-12-20 GMT" "2013-12-21 GMT" "2013-12-22 GMT"
##  [357] "2013-12-23 GMT" "2013-12-24 GMT" "2013-12-25 GMT" "2013-12-26 GMT"
##  [361] "2013-12-27 GMT" "2013-12-28 GMT" "2013-12-29 GMT" "2013-12-30 GMT"
##  [365] "2013-12-31 GMT" "2014-01-01 GMT" "2014-01-02 GMT" "2014-01-03 GMT"
##  [369] "2014-01-04 GMT" "2014-01-05 GMT" "2014-01-06 GMT" "2014-01-07 GMT"
##  [373] "2014-01-08 GMT" "2014-01-09 GMT" "2014-01-10 GMT" "2014-01-11 GMT"
##  [377] "2014-01-12 GMT" "2014-01-13 GMT" "2014-01-14 GMT" "2014-01-15 GMT"
##  [381] "2014-01-16 GMT" "2014-01-17 GMT" "2014-01-18 GMT" "2014-01-19 GMT"
##  [385] "2014-01-20 GMT" "2014-01-21 GMT" "2014-01-22 GMT" "2014-01-23 GMT"
##  [389] "2014-01-24 GMT" "2014-01-25 GMT" "2014-01-26 GMT" "2014-01-27 GMT"
##  [393] "2014-01-28 GMT" "2014-01-29 GMT" "2014-01-30 GMT" "2014-01-31 GMT"
##  [397] "2014-02-01 GMT" "2014-02-02 GMT" "2014-02-03 GMT" "2014-02-04 GMT"
##  [401] "2014-02-05 GMT" "2014-02-06 GMT" "2014-02-07 GMT" "2014-02-08 GMT"
##  [405] "2014-02-09 GMT" "2014-02-10 GMT" "2014-02-11 GMT" "2014-02-12 GMT"
##  [409] "2014-02-13 GMT" "2014-02-14 GMT" "2014-02-15 GMT" "2014-02-16 GMT"
##  [413] "2014-02-17 GMT" "2014-02-18 GMT" "2014-02-19 GMT" "2014-02-20 GMT"
##  [417] "2014-02-21 GMT" "2014-02-22 GMT" "2014-02-23 GMT" "2014-02-24 GMT"
##  [421] "2014-02-25 GMT" "2014-02-26 GMT" "2014-02-27 GMT" "2014-02-28 GMT"
##  [425] "2014-03-01 GMT" "2014-03-02 GMT" "2014-03-03 GMT" "2014-03-04 GMT"
##  [429] "2014-03-05 GMT" "2014-03-06 GMT" "2014-03-07 GMT" "2014-03-08 GMT"
##  [433] "2014-03-09 GMT" "2014-03-10 GMT" "2014-03-11 GMT" "2014-03-12 GMT"
##  [437] "2014-03-13 GMT" "2014-03-14 GMT" "2014-03-15 GMT" "2014-03-16 GMT"
##  [441] "2014-03-17 GMT" "2014-03-18 GMT" "2014-03-19 GMT" "2014-03-20 GMT"
##  [445] "2014-03-21 GMT" "2014-03-22 GMT" "2014-03-23 GMT" "2014-03-24 GMT"
##  [449] "2014-03-25 GMT" "2014-03-26 GMT" "2014-03-27 GMT" "2014-03-28 GMT"
##  [453] "2014-03-29 GMT" "2014-03-30 GMT" "2014-03-31 GMT" "2014-04-01 GMT"
##  [457] "2014-04-02 GMT" "2014-04-03 GMT" "2014-04-04 GMT" "2014-04-05 GMT"
##  [461] "2014-04-06 GMT" "2014-04-07 GMT" "2014-04-08 GMT" "2014-04-09 GMT"
##  [465] "2014-04-10 GMT" "2014-04-11 GMT" "2014-04-12 GMT" "2014-04-13 GMT"
##  [469] "2014-04-14 GMT" "2014-04-15 GMT" "2014-04-16 GMT" "2014-04-17 GMT"
##  [473] "2014-04-18 GMT" "2014-04-19 GMT" "2014-04-20 GMT" "2014-04-21 GMT"
##  [477] "2014-04-22 GMT" "2014-04-23 GMT" "2014-04-24 GMT" "2014-04-25 GMT"
##  [481] "2014-04-26 GMT" "2014-04-27 GMT" "2014-04-28 GMT" "2014-04-29 GMT"
##  [485] "2014-04-30 GMT" "2014-05-01 GMT" "2014-05-02 GMT" "2014-05-03 GMT"
##  [489] "2014-05-04 GMT" "2014-05-05 GMT" "2014-05-06 GMT" "2014-05-07 GMT"
##  [493] "2014-05-08 GMT" "2014-05-09 GMT" "2014-05-10 GMT" "2014-05-11 GMT"
##  [497] "2014-05-12 GMT" "2014-05-13 GMT" "2014-05-14 GMT" "2014-05-15 GMT"
##  [501] "2014-05-16 GMT" "2014-05-17 GMT" "2014-05-18 GMT" "2014-05-19 GMT"
##  [505] "2014-05-20 GMT" "2014-05-21 GMT" "2014-05-22 GMT" "2014-05-23 GMT"
##  [509] "2014-05-24 GMT" "2014-05-25 GMT" "2014-05-26 GMT" "2014-05-27 GMT"
##  [513] "2014-05-28 GMT" "2014-05-29 GMT" "2014-05-30 GMT" "2014-05-31 GMT"
##  [517] "2014-06-01 GMT" "2014-06-02 GMT" "2014-06-03 GMT" "2014-06-04 GMT"
##  [521] "2014-06-05 GMT" "2014-06-06 GMT" "2014-06-07 GMT" "2014-06-08 GMT"
##  [525] "2014-06-09 GMT" "2014-06-10 GMT" "2014-06-11 GMT" "2014-06-12 GMT"
##  [529] "2014-06-13 GMT" "2014-06-14 GMT" "2014-06-15 GMT" "2014-06-16 GMT"
##  [533] "2014-06-17 GMT" "2014-06-18 GMT" "2014-06-19 GMT" "2014-06-20 GMT"
##  [537] "2014-06-21 GMT" "2014-06-22 GMT" "2014-06-23 GMT" "2014-06-24 GMT"
##  [541] "2014-06-25 GMT" "2014-06-26 GMT" "2014-06-27 GMT" "2014-06-28 GMT"
##  [545] "2014-06-29 GMT" "2014-06-30 GMT" "2014-07-01 GMT" "2014-07-02 GMT"
##  [549] "2014-07-03 GMT" "2014-07-04 GMT" "2014-07-05 GMT" "2014-07-06 GMT"
##  [553] "2014-07-07 GMT" "2014-07-08 GMT" "2014-07-09 GMT" "2014-07-10 GMT"
##  [557] "2014-07-11 GMT" "2014-07-12 GMT" "2014-07-13 GMT" "2014-07-14 GMT"
##  [561] "2014-07-15 GMT" "2014-07-16 GMT" "2014-07-17 GMT" "2014-07-18 GMT"
##  [565] "2014-07-19 GMT" "2014-07-20 GMT" "2014-07-21 GMT" "2014-07-22 GMT"
##  [569] "2014-07-23 GMT" "2014-07-24 GMT" "2014-07-25 GMT" "2014-07-26 GMT"
##  [573] "2014-07-27 GMT" "2014-07-28 GMT" "2014-07-29 GMT" "2014-07-30 GMT"
##  [577] "2014-07-31 GMT" "2014-08-01 GMT" "2014-08-02 GMT" "2014-08-03 GMT"
##  [581] "2014-08-04 GMT" "2014-08-05 GMT" "2014-08-06 GMT" "2014-08-07 GMT"
##  [585] "2014-08-08 GMT" "2014-08-09 GMT" "2014-08-10 GMT" "2014-08-11 GMT"
##  [589] "2014-08-12 GMT" "2014-08-13 GMT" "2014-08-14 GMT" "2014-08-15 GMT"
##  [593] "2014-08-16 GMT" "2014-08-17 GMT" "2014-08-18 GMT" "2014-08-19 GMT"
##  [597] "2014-08-20 GMT" "2014-08-21 GMT" "2014-08-22 GMT" "2014-08-23 GMT"
##  [601] "2014-08-24 GMT" "2014-08-25 GMT" "2014-08-26 GMT" "2014-08-27 GMT"
##  [605] "2014-08-28 GMT" "2014-08-29 GMT" "2014-08-30 GMT" "2014-08-31 GMT"
##  [609] "2014-09-01 GMT" "2014-09-02 GMT" "2014-09-03 GMT" "2014-09-04 GMT"
##  [613] "2014-09-05 GMT" "2014-09-06 GMT" "2014-09-07 GMT" "2014-09-08 GMT"
##  [617] "2014-09-09 GMT" "2014-09-10 GMT" "2014-09-11 GMT" "2014-09-12 GMT"
##  [621] "2014-09-13 GMT" "2014-09-14 GMT" "2014-09-15 GMT" "2014-09-16 GMT"
##  [625] "2014-09-17 GMT" "2014-09-18 GMT" "2014-09-19 GMT" "2014-09-20 GMT"
##  [629] "2014-09-21 GMT" "2014-09-22 GMT" "2014-09-23 GMT" "2014-09-24 GMT"
##  [633] "2014-09-25 GMT" "2014-09-26 GMT" "2014-09-27 GMT" "2014-09-28 GMT"
##  [637] "2014-09-29 GMT" "2014-09-30 GMT" "2014-10-01 GMT" "2014-10-02 GMT"
##  [641] "2014-10-03 GMT" "2014-10-04 GMT" "2014-10-05 GMT" "2014-10-06 GMT"
##  [645] "2014-10-07 GMT" "2014-10-08 GMT" "2014-10-09 GMT" "2014-10-10 GMT"
##  [649] "2014-10-11 GMT" "2014-10-12 GMT" "2014-10-13 GMT" "2014-10-14 GMT"
##  [653] "2014-10-15 GMT" "2014-10-16 GMT" "2014-10-17 GMT" "2014-10-18 GMT"
##  [657] "2014-10-19 GMT" "2014-10-20 GMT" "2014-10-21 GMT" "2014-10-22 GMT"
##  [661] "2014-10-23 GMT" "2014-10-24 GMT" "2014-10-25 GMT" "2014-10-26 GMT"
##  [665] "2014-10-27 GMT" "2014-10-28 GMT" "2014-10-29 GMT" "2014-10-30 GMT"
##  [669] "2014-10-31 GMT" "2014-11-01 GMT" "2014-11-02 GMT" "2014-11-03 GMT"
##  [673] "2014-11-04 GMT" "2014-11-05 GMT" "2014-11-06 GMT" "2014-11-07 GMT"
##  [677] "2014-11-08 GMT" "2014-11-09 GMT" "2014-11-10 GMT" "2014-11-11 GMT"
##  [681] "2014-11-12 GMT" "2014-11-13 GMT" "2014-11-14 GMT" "2014-11-15 GMT"
##  [685] "2014-11-16 GMT" "2014-11-17 GMT" "2014-11-18 GMT" "2014-11-19 GMT"
##  [689] "2014-11-20 GMT" "2014-11-21 GMT" "2014-11-22 GMT" "2014-11-23 GMT"
##  [693] "2014-11-24 GMT" "2014-11-25 GMT" "2014-11-26 GMT" "2014-11-27 GMT"
##  [697] "2014-11-28 GMT" "2014-11-29 GMT" "2014-11-30 GMT" "2014-12-01 GMT"
##  [701] "2014-12-02 GMT" "2014-12-03 GMT" "2014-12-04 GMT" "2014-12-05 GMT"
##  [705] "2014-12-06 GMT" "2014-12-07 GMT" "2014-12-08 GMT" "2014-12-09 GMT"
##  [709] "2014-12-10 GMT" "2014-12-11 GMT" "2014-12-12 GMT" "2014-12-13 GMT"
##  [713] "2014-12-14 GMT" "2014-12-15 GMT" "2014-12-16 GMT" "2014-12-17 GMT"
##  [717] "2014-12-18 GMT" "2014-12-19 GMT" "2014-12-20 GMT" "2014-12-21 GMT"
##  [721] "2014-12-22 GMT" "2014-12-23 GMT" "2014-12-24 GMT" "2014-12-25 GMT"
##  [725] "2014-12-26 GMT" "2014-12-27 GMT" "2014-12-28 GMT" "2014-12-29 GMT"
##  [729] "2014-12-30 GMT" "2014-12-31 GMT" "2015-01-01 GMT" "2015-01-02 GMT"
##  [733] "2015-01-03 GMT" "2015-01-04 GMT" "2015-01-05 GMT" "2015-01-06 GMT"
##  [737] "2015-01-07 GMT" "2015-01-08 GMT" "2015-01-09 GMT" "2015-01-10 GMT"
##  [741] "2015-01-11 GMT" "2015-01-12 GMT" "2015-01-13 GMT" "2015-01-14 GMT"
##  [745] "2015-01-15 GMT" "2015-01-16 GMT" "2015-01-17 GMT" "2015-01-18 GMT"
##  [749] "2015-01-19 GMT" "2015-01-20 GMT" "2015-01-21 GMT" "2015-01-22 GMT"
##  [753] "2015-01-23 GMT" "2015-01-24 GMT" "2015-01-25 GMT" "2015-01-26 GMT"
##  [757] "2015-01-27 GMT" "2015-01-28 GMT" "2015-01-29 GMT" "2015-01-30 GMT"
##  [761] "2015-01-31 GMT" "2015-02-01 GMT" "2015-02-02 GMT" "2015-02-03 GMT"
##  [765] "2015-02-04 GMT" "2015-02-05 GMT" "2015-02-06 GMT" "2015-02-07 GMT"
##  [769] "2015-02-08 GMT" "2015-02-09 GMT" "2015-02-10 GMT" "2015-02-11 GMT"
##  [773] "2015-02-12 GMT" "2015-02-13 GMT" "2015-02-14 GMT" "2015-02-15 GMT"
##  [777] "2015-02-16 GMT" "2015-02-17 GMT" "2015-02-18 GMT" "2015-02-19 GMT"
##  [781] "2015-02-20 GMT" "2015-02-21 GMT" "2015-02-22 GMT" "2015-02-23 GMT"
##  [785] "2015-02-24 GMT" "2015-02-25 GMT" "2015-02-26 GMT" "2015-02-27 GMT"
##  [789] "2015-02-28 GMT" "2015-03-01 GMT" "2015-03-02 GMT" "2015-03-03 GMT"
##  [793] "2015-03-04 GMT" "2015-03-05 GMT" "2015-03-06 GMT" "2015-03-07 GMT"
##  [797] "2015-03-08 GMT" "2015-03-09 GMT" "2015-03-10 GMT" "2015-03-11 GMT"
##  [801] "2015-03-12 GMT" "2015-03-13 GMT" "2015-03-14 GMT" "2015-03-15 GMT"
##  [805] "2015-03-16 GMT" "2015-03-17 GMT" "2015-03-18 GMT" "2015-03-19 GMT"
##  [809] "2015-03-20 GMT" "2015-03-21 GMT" "2015-03-22 GMT" "2015-03-23 GMT"
##  [813] "2015-03-24 GMT" "2015-03-25 GMT" "2015-03-26 GMT" "2015-03-27 GMT"
##  [817] "2015-03-28 GMT" "2015-03-29 GMT" "2015-03-30 GMT" "2015-03-31 GMT"
##  [821] "2015-04-01 GMT" "2015-04-02 GMT" "2015-04-03 GMT" "2015-04-04 GMT"
##  [825] "2015-04-05 GMT" "2015-04-06 GMT" "2015-04-07 GMT" "2015-04-08 GMT"
##  [829] "2015-04-09 GMT" "2015-04-10 GMT" "2015-04-11 GMT" "2015-04-12 GMT"
##  [833] "2015-04-13 GMT" "2015-04-14 GMT" "2015-04-15 GMT" "2015-04-16 GMT"
##  [837] "2015-04-17 GMT" "2015-04-18 GMT" "2015-04-19 GMT" "2015-04-20 GMT"
##  [841] "2015-04-21 GMT" "2015-04-22 GMT" "2015-04-23 GMT" "2015-04-24 GMT"
##  [845] "2015-04-25 GMT" "2015-04-26 GMT" "2015-04-27 GMT" "2015-04-28 GMT"
##  [849] "2015-04-29 GMT" "2015-04-30 GMT" "2015-05-01 GMT" "2015-05-02 GMT"
##  [853] "2015-05-03 GMT" "2015-05-04 GMT" "2015-05-05 GMT" "2015-05-06 GMT"
##  [857] "2015-05-07 GMT" "2015-05-08 GMT" "2015-05-09 GMT" "2015-05-10 GMT"
##  [861] "2015-05-11 GMT" "2015-05-12 GMT" "2015-05-13 GMT" "2015-05-14 GMT"
##  [865] "2015-05-15 GMT" "2015-05-16 GMT" "2015-05-17 GMT" "2015-05-18 GMT"
##  [869] "2015-05-19 GMT" "2015-05-20 GMT" "2015-05-21 GMT" "2015-05-22 GMT"
##  [873] "2015-05-23 GMT" "2015-05-24 GMT" "2015-05-25 GMT" "2015-05-26 GMT"
##  [877] "2015-05-27 GMT" "2015-05-28 GMT" "2015-05-29 GMT" "2015-05-30 GMT"
##  [881] "2015-05-31 GMT" "2015-06-01 GMT" "2015-06-02 GMT" "2015-06-03 GMT"
##  [885] "2015-06-04 GMT" "2015-06-05 GMT" "2015-06-06 GMT" "2015-06-07 GMT"
##  [889] "2015-06-08 GMT" "2015-06-09 GMT" "2015-06-10 GMT" "2015-06-11 GMT"
##  [893] "2015-06-12 GMT" "2015-06-13 GMT" "2015-06-14 GMT" "2015-06-15 GMT"
##  [897] "2015-06-16 GMT" "2015-06-17 GMT" "2015-06-18 GMT" "2015-06-19 GMT"
##  [901] "2015-06-20 GMT" "2015-06-21 GMT" "2015-06-22 GMT" "2015-06-23 GMT"
##  [905] "2015-06-24 GMT" "2015-06-25 GMT" "2015-06-26 GMT" "2015-06-27 GMT"
##  [909] "2015-06-28 GMT" "2015-06-29 GMT" "2015-06-30 GMT" "2015-07-01 GMT"
##  [913] "2015-07-02 GMT" "2015-07-03 GMT" "2015-07-04 GMT" "2015-07-05 GMT"
##  [917] "2015-07-06 GMT" "2015-07-07 GMT" "2015-07-08 GMT" "2015-07-09 GMT"
##  [921] "2015-07-10 GMT" "2015-07-11 GMT" "2015-07-12 GMT" "2015-07-13 GMT"
##  [925] "2015-07-14 GMT" "2015-07-15 GMT" "2015-07-16 GMT" "2015-07-17 GMT"
##  [929] "2015-07-18 GMT" "2015-07-19 GMT" "2015-07-20 GMT" "2015-07-21 GMT"
##  [933] "2015-07-22 GMT" "2015-07-23 GMT" "2015-07-24 GMT" "2015-07-25 GMT"
##  [937] "2015-07-26 GMT" "2015-07-27 GMT" "2015-07-28 GMT" "2015-07-29 GMT"
##  [941] "2015-07-30 GMT" "2015-07-31 GMT" "2015-08-01 GMT" "2015-08-02 GMT"
##  [945] "2015-08-03 GMT" "2015-08-04 GMT" "2015-08-05 GMT" "2015-08-06 GMT"
##  [949] "2015-08-07 GMT" "2015-08-08 GMT" "2015-08-09 GMT" "2015-08-10 GMT"
##  [953] "2015-08-11 GMT" "2015-08-12 GMT" "2015-08-13 GMT" "2015-08-14 GMT"
##  [957] "2015-08-15 GMT" "2015-08-16 GMT" "2015-08-17 GMT" "2015-08-18 GMT"
##  [961] "2015-08-19 GMT" "2015-08-20 GMT" "2015-08-21 GMT" "2015-08-22 GMT"
##  [965] "2015-08-23 GMT" "2015-08-24 GMT" "2015-08-25 GMT" "2015-08-26 GMT"
##  [969] "2015-08-27 GMT" "2015-08-28 GMT" "2015-08-29 GMT" "2015-08-30 GMT"
##  [973] "2015-08-31 GMT" "2015-09-01 GMT" "2015-09-02 GMT" "2015-09-03 GMT"
##  [977] "2015-09-04 GMT" "2015-09-05 GMT" "2015-09-06 GMT" "2015-09-07 GMT"
##  [981] "2015-09-08 GMT" "2015-09-09 GMT" "2015-09-10 GMT" "2015-09-11 GMT"
##  [985] "2015-09-12 GMT" "2015-09-13 GMT" "2015-09-14 GMT" "2015-09-15 GMT"
##  [989] "2015-09-16 GMT" "2015-09-17 GMT" "2015-09-18 GMT" "2015-09-19 GMT"
##  [993] "2015-09-20 GMT" "2015-09-21 GMT" "2015-09-22 GMT" "2015-09-23 GMT"
##  [997] "2015-09-24 GMT" "2015-09-25 GMT" "2015-09-26 GMT" "2015-09-27 GMT"
## [1001] "2015-09-28 GMT" "2015-09-29 GMT" "2015-09-30 GMT" "2015-10-01 GMT"
## [1005] "2015-10-02 GMT" "2015-10-03 GMT" "2015-10-04 GMT" "2015-10-05 GMT"
## [1009] "2015-10-06 GMT" "2015-10-07 GMT" "2015-10-08 GMT" "2015-10-09 GMT"
## [1013] "2015-10-10 GMT" "2015-10-11 GMT" "2015-10-12 GMT" "2015-10-13 GMT"
## [1017] "2015-10-14 GMT" "2015-10-15 GMT" "2015-10-16 GMT" "2015-10-17 GMT"
## [1021] "2015-10-18 GMT" "2015-10-19 GMT" "2015-10-20 GMT" "2015-10-21 GMT"
## [1025] "2015-10-22 GMT" "2015-10-23 GMT" "2015-10-24 GMT" "2015-10-25 GMT"
## [1029] "2015-10-26 GMT" "2015-10-27 GMT" "2015-10-28 GMT" "2015-10-29 GMT"
## [1033] "2015-10-30 GMT" "2015-10-31 GMT" "2015-11-01 GMT" "2015-11-02 GMT"
## [1037] "2015-11-03 GMT" "2015-11-04 GMT" "2015-11-05 GMT" "2015-11-06 GMT"
## [1041] "2015-11-07 GMT" "2015-11-08 GMT" "2015-11-09 GMT" "2015-11-10 GMT"
## [1045] "2015-11-11 GMT" "2015-11-12 GMT" "2015-11-13 GMT" "2015-11-14 GMT"
## [1049] "2015-11-15 GMT" "2015-11-16 GMT" "2015-11-17 GMT" "2015-11-18 GMT"
## [1053] "2015-11-19 GMT" "2015-11-20 GMT" "2015-11-21 GMT" "2015-11-22 GMT"
## [1057] "2015-11-23 GMT" "2015-11-24 GMT" "2015-11-25 GMT" "2015-11-26 GMT"
## [1061] "2015-11-27 GMT" "2015-11-28 GMT" "2015-11-29 GMT" "2015-11-30 GMT"
## [1065] "2015-12-01 GMT" "2015-12-02 GMT" "2015-12-03 GMT" "2015-12-04 GMT"
## [1069] "2015-12-05 GMT" "2015-12-06 GMT" "2015-12-07 GMT" "2015-12-08 GMT"
## [1073] "2015-12-09 GMT" "2015-12-10 GMT" "2015-12-11 GMT" "2015-12-12 GMT"
## [1077] "2015-12-13 GMT" "2015-12-14 GMT" "2015-12-15 GMT" "2015-12-16 GMT"
## [1081] "2015-12-17 GMT" "2015-12-18 GMT" "2015-12-19 GMT" "2015-12-20 GMT"
## [1085] "2015-12-21 GMT" "2015-12-22 GMT" "2015-12-23 GMT" "2015-12-24 GMT"
## [1089] "2015-12-25 GMT" "2015-12-26 GMT" "2015-12-27 GMT" "2015-12-28 GMT"
## [1093] "2015-12-29 GMT" "2015-12-30 GMT" "2015-12-31 GMT" "2016-01-01 GMT"
## [1097] "2016-01-02 GMT" "2016-01-03 GMT" "2016-01-04 GMT" "2016-01-05 GMT"
## [1101] "2016-01-06 GMT" "2016-01-07 GMT" "2016-01-08 GMT" "2016-01-09 GMT"
## [1105] "2016-01-10 GMT" "2016-01-11 GMT" "2016-01-12 GMT" "2016-01-13 GMT"
## [1109] "2016-01-14 GMT" "2016-01-15 GMT" "2016-01-16 GMT" "2016-01-17 GMT"
## [1113] "2016-01-18 GMT" "2016-01-19 GMT" "2016-01-20 GMT" "2016-01-21 GMT"
## [1117] "2016-01-22 GMT" "2016-01-23 GMT" "2016-01-24 GMT" "2016-01-25 GMT"
## [1121] "2016-01-26 GMT" "2016-01-27 GMT" "2016-01-28 GMT" "2016-01-29 GMT"
## [1125] "2016-01-30 GMT" "2016-01-31 GMT" "2016-02-01 GMT" "2016-02-02 GMT"
## [1129] "2016-02-03 GMT" "2016-02-04 GMT" "2016-02-05 GMT" "2016-02-06 GMT"
## [1133] "2016-02-07 GMT" "2016-02-08 GMT" "2016-02-09 GMT" "2016-02-10 GMT"
## [1137] "2016-02-11 GMT" "2016-02-12 GMT" "2016-02-13 GMT" "2016-02-14 GMT"
## [1141] "2016-02-15 GMT" "2016-02-16 GMT" "2016-02-17 GMT" "2016-02-18 GMT"
## [1145] "2016-02-19 GMT" "2016-02-20 GMT" "2016-02-21 GMT" "2016-02-22 GMT"
## [1149] "2016-02-23 GMT" "2016-02-24 GMT" "2016-02-25 GMT" "2016-02-26 GMT"
## [1153] "2016-02-27 GMT" "2016-02-28 GMT" "2016-02-29 GMT" "2016-03-01 GMT"
## [1157] "2016-03-02 GMT" "2016-03-03 GMT" "2016-03-04 GMT" "2016-03-05 GMT"
## [1161] "2016-03-06 GMT" "2016-03-07 GMT" "2016-03-08 GMT" "2016-03-09 GMT"
## [1165] "2016-03-10 GMT" "2016-03-11 GMT" "2016-03-12 GMT" "2016-03-13 GMT"
## [1169] "2016-03-14 GMT" "2016-03-15 GMT" "2016-03-16 GMT" "2016-03-17 GMT"
## [1173] "2016-03-18 GMT" "2016-03-19 GMT" "2016-03-20 GMT" "2016-03-21 GMT"
## [1177] "2016-03-22 GMT" "2016-03-23 GMT" "2016-03-24 GMT" "2016-03-25 GMT"
## [1181] "2016-03-26 GMT" "2016-03-27 GMT" "2016-03-28 GMT" "2016-03-29 GMT"
## [1185] "2016-03-30 GMT" "2016-03-31 GMT" "2016-04-01 GMT" "2016-04-02 GMT"
## [1189] "2016-04-03 GMT" "2016-04-04 GMT" "2016-04-05 GMT" "2016-04-06 GMT"
## [1193] "2016-04-07 GMT" "2016-04-08 GMT" "2016-04-09 GMT" "2016-04-10 GMT"
## [1197] "2016-04-11 GMT" "2016-04-12 GMT" "2016-04-13 GMT" "2016-04-14 GMT"
## [1201] "2016-04-15 GMT" "2016-04-16 GMT" "2016-04-17 GMT" "2016-04-18 GMT"
## [1205] "2016-04-19 GMT" "2016-04-20 GMT" "2016-04-21 GMT" "2016-04-22 GMT"
## [1209] "2016-04-23 GMT" "2016-04-24 GMT" "2016-04-25 GMT" "2016-04-26 GMT"
## [1213] "2016-04-27 GMT" "2016-04-28 GMT" "2016-04-29 GMT" "2016-04-30 GMT"
## [1217] "2016-05-01 GMT" "2016-05-02 GMT" "2016-05-03 GMT" "2016-05-04 GMT"
## [1221] "2016-05-05 GMT" "2016-05-06 GMT" "2016-05-07 GMT" "2016-05-08 GMT"
## [1225] "2016-05-09 GMT" "2016-05-10 GMT" "2016-05-11 GMT" "2016-05-12 GMT"
## [1229] "2016-05-13 GMT" "2016-05-14 GMT" "2016-05-15 GMT" "2016-05-16 GMT"
## [1233] "2016-05-17 GMT" "2016-05-18 GMT" "2016-05-19 GMT" "2016-05-20 GMT"
## [1237] "2016-05-21 GMT" "2016-05-22 GMT" "2016-05-23 GMT" "2016-05-24 GMT"
## [1241] "2016-05-25 GMT" "2016-05-26 GMT" "2016-05-27 GMT" "2016-05-28 GMT"
## [1245] "2016-05-29 GMT" "2016-05-30 GMT" "2016-05-31 GMT" "2016-06-01 GMT"
## [1249] "2016-06-02 GMT" "2016-06-03 GMT" "2016-06-04 GMT" "2016-06-05 GMT"
## [1253] "2016-06-06 GMT" "2016-06-07 GMT" "2016-06-08 GMT" "2016-06-09 GMT"
## [1257] "2016-06-10 GMT" "2016-06-11 GMT" "2016-06-12 GMT" "2016-06-13 GMT"
## [1261] "2016-06-14 GMT" "2016-06-15 GMT" "2016-06-16 GMT" "2016-06-17 GMT"
## [1265] "2016-06-18 GMT" "2016-06-19 GMT" "2016-06-20 GMT" "2016-06-21 GMT"
## [1269] "2016-06-22 GMT" "2016-06-23 GMT" "2016-06-24 GMT" "2016-06-25 GMT"
## [1273] "2016-06-26 GMT" "2016-06-27 GMT" "2016-06-28 GMT" "2016-06-29 GMT"
## [1277] "2016-06-30 GMT" "2016-07-01 GMT" "2016-07-02 GMT" "2016-07-03 GMT"
## [1281] "2016-07-04 GMT" "2016-07-05 GMT" "2016-07-06 GMT" "2016-07-07 GMT"
## [1285] "2016-07-08 GMT" "2016-07-09 GMT" "2016-07-10 GMT" "2016-07-11 GMT"
## [1289] "2016-07-12 GMT" "2016-07-13 GMT" "2016-07-14 GMT" "2016-07-15 GMT"
## [1293] "2016-07-16 GMT" "2016-07-17 GMT" "2016-07-18 GMT" "2016-07-19 GMT"
## [1297] "2016-07-20 GMT" "2016-07-21 GMT" "2016-07-22 GMT" "2016-07-23 GMT"
## [1301] "2016-07-24 GMT" "2016-07-25 GMT" "2016-07-26 GMT" "2016-07-27 GMT"
## [1305] "2016-07-28 GMT" "2016-07-29 GMT" "2016-07-30 GMT" "2016-07-31 GMT"
## [1309] "2016-08-01 GMT" "2016-08-02 GMT" "2016-08-03 GMT" "2016-08-04 GMT"
## [1313] "2016-08-05 GMT" "2016-08-06 GMT" "2016-08-07 GMT" "2016-08-08 GMT"
## [1317] "2016-08-09 GMT" "2016-08-10 GMT" "2016-08-11 GMT" "2016-08-12 GMT"
## [1321] "2016-08-13 GMT" "2016-08-14 GMT" "2016-08-15 GMT" "2016-08-16 GMT"
## [1325] "2016-08-17 GMT" "2016-08-18 GMT" "2016-08-19 GMT" "2016-08-20 GMT"
## [1329] "2016-08-21 GMT" "2016-08-22 GMT" "2016-08-23 GMT" "2016-08-24 GMT"
## [1333] "2016-08-25 GMT" "2016-08-26 GMT" "2016-08-27 GMT" "2016-08-28 GMT"
## [1337] "2016-08-29 GMT" "2016-08-30 GMT" "2016-08-31 GMT" "2016-09-01 GMT"
## [1341] "2016-09-02 GMT" "2016-09-03 GMT" "2016-09-04 GMT" "2016-09-05 GMT"
## [1345] "2016-09-06 GMT" "2016-09-07 GMT" "2016-09-08 GMT" "2016-09-09 GMT"
## [1349] "2016-09-10 GMT" "2016-09-11 GMT" "2016-09-12 GMT" "2016-09-13 GMT"
## [1353] "2016-09-14 GMT" "2016-09-15 GMT" "2016-09-16 GMT" "2016-09-17 GMT"
## [1357] "2016-09-18 GMT" "2016-09-19 GMT" "2016-09-20 GMT" "2016-09-21 GMT"
## [1361] "2016-09-22 GMT" "2016-09-23 GMT" "2016-09-24 GMT" "2016-09-25 GMT"
## [1365] "2016-09-26 GMT" "2016-09-27 GMT" "2016-09-28 GMT" "2016-09-29 GMT"
## [1369] "2016-09-30 GMT" "2016-10-01 GMT" "2016-10-02 GMT" "2016-10-03 GMT"
## [1373] "2016-10-04 GMT" "2016-10-05 GMT" "2016-10-06 GMT" "2016-10-07 GMT"
## [1377] "2016-10-08 GMT" "2016-10-09 GMT" "2016-10-10 GMT" "2016-10-11 GMT"
## [1381] "2016-10-12 GMT" "2016-10-13 GMT" "2016-10-14 GMT" "2016-10-15 GMT"
## [1385] "2016-10-16 GMT" "2016-10-17 GMT" "2016-10-18 GMT" "2016-10-19 GMT"
## [1389] "2016-10-20 GMT" "2016-10-21 GMT" "2016-10-22 GMT" "2016-10-23 GMT"
## [1393] "2016-10-24 GMT" "2016-10-25 GMT" "2016-10-26 GMT" "2016-10-27 GMT"
## [1397] "2016-10-28 GMT" "2016-10-29 GMT" "2016-10-30 GMT" "2016-10-31 GMT"
## [1401] "2016-11-01 GMT" "2016-11-02 GMT" "2016-11-03 GMT" "2016-11-04 GMT"
## [1405] "2016-11-05 GMT" "2016-11-06 GMT" "2016-11-07 GMT" "2016-11-08 GMT"
## [1409] "2016-11-09 GMT" "2016-11-10 GMT" "2016-11-11 GMT" "2016-11-12 GMT"
## [1413] "2016-11-13 GMT" "2016-11-14 GMT" "2016-11-15 GMT" "2016-11-16 GMT"
## [1417] "2016-11-17 GMT" "2016-11-18 GMT" "2016-11-19 GMT" "2016-11-20 GMT"
## [1421] "2016-11-21 GMT" "2016-11-22 GMT" "2016-11-23 GMT" "2016-11-24 GMT"
## [1425] "2016-11-25 GMT" "2016-11-26 GMT" "2016-11-27 GMT" "2016-11-28 GMT"
## [1429] "2016-11-29 GMT" "2016-11-30 GMT" "2016-12-01 GMT" "2016-12-02 GMT"
## [1433] "2016-12-03 GMT" "2016-12-04 GMT" "2016-12-05 GMT" "2016-12-06 GMT"
## [1437] "2016-12-07 GMT" "2016-12-08 GMT" "2016-12-09 GMT" "2016-12-10 GMT"
## [1441] "2016-12-11 GMT" "2016-12-12 GMT" "2016-12-13 GMT" "2016-12-14 GMT"
## [1445] "2016-12-15 GMT" "2016-12-16 GMT" "2016-12-17 GMT" "2016-12-18 GMT"
## [1449] "2016-12-19 GMT" "2016-12-20 GMT" "2016-12-21 GMT" "2016-12-22 GMT"
## [1453] "2016-12-23 GMT" "2016-12-24 GMT" "2016-12-25 GMT" "2016-12-26 GMT"
## [1457] "2016-12-27 GMT" "2016-12-28 GMT" "2016-12-29 GMT" "2016-12-30 GMT"
## [1461] "2016-12-31 GMT"
## 
## $train.holiday.names
## NULL
## 
## $train.component.cols
##    additive_terms daily weekly yearly multiplicative_terms
## 1               1     0      0      1                    0
## 2               1     0      0      1                    0
## 3               1     0      0      1                    0
## 4               1     0      0      1                    0
## 5               1     0      0      1                    0
## 6               1     0      0      1                    0
## 7               1     0      0      1                    0
## 8               1     0      0      1                    0
## 9               1     0      0      1                    0
## 10              1     0      0      1                    0
## 11              1     0      0      1                    0
## 12              1     0      0      1                    0
## 13              1     0      0      1                    0
## 14              1     0      0      1                    0
## 15              1     0      0      1                    0
## 16              1     0      0      1                    0
## 17              1     0      0      1                    0
## 18              1     0      0      1                    0
## 19              1     0      0      1                    0
## 20              1     0      0      1                    0
## 21              1     0      1      0                    0
## 22              1     0      1      0                    0
## 23              1     0      1      0                    0
## 24              1     0      1      0                    0
## 25              1     0      1      0                    0
## 26              1     0      1      0                    0
## 27              1     1      0      0                    0
## 28              1     1      0      0                    0
## 29              1     1      0      0                    0
## 30              1     1      0      0                    0
## 31              1     1      0      0                    0
## 32              1     1      0      0                    0
## 33              1     1      0      0                    0
## 34              1     1      0      0                    0
## 
## $component.modes
## $component.modes$additive
## [1] "yearly"                    "weekly"                   
## [3] "daily"                     "additive_terms"           
## [5] "extra_regressors_additive" "holidays"                 
## 
## $component.modes$multiplicative
## [1] "multiplicative_terms"            "extra_regressors_multiplicative"
## 
## 
## $fit.kwargs
## list()
## 
## attr(,"class")
## [1] "prophet" "list"

Berdasarkan hasil fitting model diatas bisa dijelaslkan bahwa model_ts sekarang menyimpan informasi data permintaan harian pada store 03. Sehingga kita bisa gunakan untuk mengekstrak informasi deret waktu tersebut untuk melakukan perkiraan selama periode waktu yang bisa ditentukan. Misalnya kita akan memperkiraan permintaan penjualan untuk 1 tahun kedepan. Utuk melakukan ini kita harus menyiapkan data frame yang terdiri dari rentang waktu/tanggal mendatang yang akan diperkirakan. Untungnya dalam prophet() sudah menyediakan sebuah fungsi make_future_dataframe() memudahkan kita untuk menyiapkan data tersebut.

range(train_daily_3$ds)

## [1] "2013-01-01" "2016-12-31"

Bisa dilihat bahwa jangka waktu prediksi mulai dari 2013 s/d 2016

Menyiapkan tanggal untuk prediksi

Periode prediksi adalah 1 tahun kedepan atau 365 hari

# menyiapkan tanggal utk prediksi
future_ts <- make_future_dataframe(model_ts, periods = 365, freq = "day")
glimpse(future_ts)

## Rows: 1,826
## Columns: 1
## $ ds <dttm> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0~

Visualisasi hasil forecasting untuk perkiraan data 1 tahun kedepan

# visualisasi hasil forecasting
forecast_ts <- predict(model_ts, future_ts)
plot(model_ts, forecast_ts)

Bisa dilihat bahwa, gambar pada grafik yang berwarna biru menunjukkan hasil forecast yang sudah dilakukan. Titik hitam menunjukkan data dari mulai 2013 sampai 2016. Waktu biru yang tidak ada titik adalah perkiraan permintaan untuk 2017

Visualisasi komponen model

Dengan prophet dimungkinkan kita memvisulisasikan berdasarkan trend, weekly, dan yearly. Default: - daily: sampling hourly, dan frequency 24 - weekly: sampling daily, dan frequency 7 - yearly: sampling daily dan frequency 365

#visualiasi komponen model
prophet_plot_components(model_ts, forecast_ts)

Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:

• Penjualan dari tahun ke tahun meningkat, dimana penjualan di tahun 2017 adalah penjualan yang tertinggi
• Penjualan terbanyak pada setiap bulan dan tahun cendrung mengalami peningkatan di hari weekend, yaitu hari Jumat, Sabtu dan Minggu, sementara penjualan di hari Senin adalah penjualan terendah dibandingakan dengn hari yang lain
• Periode penjualan dalam setahun yang paling tinggi adalah pada bulan Juni, Juli dan Agustus, sedangkan tingkat penjualan terendah pada bulan Januari

forecast berdasarkan seasionality bulan

# forecast berdasarkan seasionality month (bulan)
model_ts_monthly <- prophet(changepoint.prior.scale = 0.05, 
                    yearly.seasonality = FALSE) %>% 
  add_seasonality(name = "monthly", period = 30.5, fourier.order = 3) %>% 
  fit.prophet(train_daily_3) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_ts_monthly <- make_future_dataframe(model_ts_monthly, periods = 365) 
forecast_ts_monthly <- predict(model_ts_monthly, future_ts_monthly) 
prophet_plot_components(model_ts_monthly, forecast_ts_monthly)

Visualisasi trend permintaan

Dalam kasus ini kita akan memvisualisasi tren permintaan dari awal tahun 2017 sampai akhir 2017

#visualisasi dari tren awal 2017 sampai akhir 2017
plot(model_ts_monthly, forecast_ts_monthly)

Bisa dilihat bahwa terjadi nya trend peningkatan permintaan yang relatif tinggi dibandingkan tahun sebelumnya

forecast berdasarkan seasionality penambahan holiday (hari libur)

# Menetapkan hari libur mulai dari tahun 2013 sampai 2016, misal libur di hari natal 25 desember atau tahun baru setiap tanggal 31 desember
holiday <- 
  data.frame( 
    holiday = "newyeareve", 
    ds = dmy(c("31-12-2013","31-12-2014", "31-12-2015", "31-12-2016", "31-12-2017")), 
    lower_window = -5, 
    upper_window = 0 
  ) 
holiday 

# visualisasi hasil forecast dengan penambahan efek holiday
model_ts_holiday <- prophet(changepoint.prior.scale = 0.05, 
                    holidays = holiday) %>% 
  add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>% 
  fit.prophet(train_daily_3) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_ts_holiday <- make_future_dataframe(model_ts_holiday, periods = 365) 
forecast_ts_holiday <- predict(model_ts_holiday, future_ts_holiday) 
plot(model_ts_holiday, forecast_ts_holiday)

# melihat trend dan holiday effect dari perkiraan
prophet_plot_components(model_ts_holiday, forecast_ts_holiday)

Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:

1. Berdasarkan penjualan mingguan didapatkan bahwa penjualan meningkat diawal bulan
2. Dengan menambahkan seasionality holiday didapatkan bahwa trend peningkatan penjualan berada pada akhir tahun yaitu dibulan desember-januari

Melihat hasil perkiraan berdasarkan trend dan seonality

forecast_ts %>%
  select(ds, trend, weekly, yearly, yhat)

Model fine Tuning untuk melihat trend liner dari permintaan

Ini digunakan untuk melihat trend perkiraan dengan bentuk lain yaitu dengan menambahkan changepoint

plot(model_ts, forecast_ts) + 
  add_changepoints_to_plot(model_ts, threshold = 0) 

Garis merah putus-putus menunjukkan change point dari trend

before_2017 <- daily_demandstore03 %>% 
  mutate( 
    year = year(date) 
  ) %>% 
  filter(year < 2017) %>% 
  rename( 
    ds = "date", 
    y = "demand" 
  ) 

after_2017 <- daily_demandstore03 %>% 
  mutate( 
    year = year(date) 
  ) %>% 
  filter(year >= 2017) %>% 
  rename( 
    ds = "date", 
    y = "demand" 
  ) 
ggplot(before_2017, aes(x=ds, y=y)) + 
  geom_point() + 
  theme_minimal()

# Model sebelum 2017 dan visualisasinya
model_before_2017 <- prophet(yearly.seasonality = TRUE, 
                             changepoint.prior.scale = 0.01) %>% 
  fit.prophet(before_2017) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_before_2017 <- make_future_dataframe(model_before_2017, periods = 365) 
forecaset_before_2017 <- predict(model_before_2017, future_before_2017) 
plot(model_before_2017, forecaset_before_2017) + 
  add_changepoints_to_plot(model_before_2017) + 
  geom_point(data = after_2017, aes(x = as.POSIXct(ds), y=y), color = "tomato3")

# Melihat transaksi paling banyak dalam satu minggu
forecast_ts %>% 
  mutate( 
    weekday = wday(ds, label = TRUE), 
    weekly = round(weekly, 5) 
  ) %>% 
  filter(ds <= max(daily_demandstore03$date)) %>% 
  select(weekday, weekly) %>% 
  distinct() %>% 
  arrange(-weekly)

## Warning in base::check_tzones(e1, e2): 'tzone' attributes are inconsistent

# Visualisasi Model Sebelum Tahun 2017 berdasarkan hari dalam satu minggu
daily_demandstore03 %>% 
  mutate( 
    wday = wday(date, label = TRUE) 
  ) %>% 
  ggplot(aes(x=date, y=demand)) + 
  geom_point(aes(color=wday)) 

Berdasarkan visualisasi diatas dapat disumpulan bahwa penjualan tertinggi pada tiap tahun ada pada hari Jumat, Sabtu dan Minggu

Model Evalution

Untuk melakukan evaluasi dari model yang sudah disiapkan, maka kita bisa menguji model tersebut pada data testing.

# Menyiapkan data
test <- read.csv("data/test.csv")
glimpse(test)

## Rows: 182,500
## Columns: 4
## $ date  <chr> "2017-01-01", "2017-01-02", "2017-01-03", "2017-01-04", "2017-01~
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ item  <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ sales <int> 19, 15, 10, 16, 14, 24, 14, 20, 18, 11, 14, 17, 7, 16, 29, 15, 1~

ada 182500 baris dan 4 kolom untuk data testing

# Merubah type data tanggal menjadi date
test %>% 
  mutate (date = as.Date(date)) %>%
  group_by(date) %>% 
  summarise( 
    demand=sum(sales)
  )

Bisa dilihat bahwa semua data testing ada pada tahun 2017.

Kita akan bandingkan data set Test dengan data set Training utk data sebelum tahun 2018, karena data train hanya sampai akhir 2016

cutoff <- dmy("01-01-2016") 
train <- daily_demandstore03 %>% 
  filter( 
    date < cutoff 
  ) %>% 
  rename( 
    "ds" = date, 
    "y" = demand 
  ) 
test <- daily_demandstore03 %>% 
  filter( 
    date >= cutoff 
  ) %>% 
  rename( 
    "ds" = date, 
    "y" = demand 
  ) 
ggplot(daily_demandstore03, aes(x=date, y=demand)) + 
  geom_point(data = train, aes(x=ds, y=y)) + 
  geom_point(data = test, aes(x=ds, y=y), color="tomato3")

Warna hitam adalah data training dan warna merah adalah data testing

Model Final

Model final digunakan untuk mempredisi data testing

# Menyiapkan model final
model_final <- prophet(changepoint.prior.scale = 0.05, 
                       yearly.seasonality = TRUE, 
                       holidays = holiday) %>% 
  add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>% 
  fit.prophet(train) 

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future_final <- make_future_dataframe(model_final, periods = nrow(test) + 1) 
forecast_final <- predict(model_final, future_final) 
plot(model_final, forecast_final)

Visual Model Final dengan data testing

plot(model_final, forecast_final) + 
  geom_point(data = test %>% 
               mutate(ds = as.POSIXct(ds)), aes(x=ds, y=y), color="tomato3")

Bisa dilihat bahwa model dapat memprediksi data testing dan sama dengan trend yang sudah diperkirakan sebelumnya.

Menghitung Akurasi dari Model

Untuk menentukan tingkat akurasi model, biasanya menghitung terlebih dulu nilai MAPE dari model. MAPE adalah Mean Absolute Persentase Error biasanya digunakan mengavaluasi model deret waktu.

eval <- test %>% 
  mutate( 
    ds = as.POSIXct(ds) 
  ) %>% 
  left_join(forecast_final) %>% 
  select(ds, y, yhat, yhat_upper, yhat_lower) 

## Joining, by = "ds"

eval 

Untuk mendapatkan nilai mape kita harus mengurangi nilai sebenarnya dengan nilai yang ada pada data testing (yhat) yang ada dalam data frame forecast_final

mape <- function(y, yhat) { 
  return(mean(abs(y - yhat)/ y)) 
} 
mape(eval$y, eval$yhat)

## [1] 0.04432686

Bisa dilihat bahwa nilai MAPE dari model adalah 0.04, sehingga akurasi dari model adalah 0,96 (96%). Jadi bisa disimpulkan bahwa model sangat akurat dalam melakukan prediksi.